THE  LIBRARY 

OF 

THE  UNIVERSITY 
OF  CALIFORNIA 

LOS  ANGELES 


PRINCIPLES   OF   SECONDARY 
EDUCATION 


THE  MACMILLAN  COMPANY 

NEW  YORK   •    BOSTON  •    CHICAGO 
DALLAS   •    SAN   FRANCISCO 

MACMILLAN  &  CO.,  LIMITED 

LONDON  •    BOMBAY  •    CALCUTTA 
MELBOURNE 

THE  MACMILLAN  CO.  OF  CANADA,  LTD. 

TORONTO 


PRINCIPLES 

OF 

SECONDARY   EDUCATION 

A  TEXT-BOOK 


BY 


CHARLES   DEGARMO 

PROFESSOR  OF  THE  SCIENCE  AND  ART  OF  EDUCATION 
CORNELL  UNIVERSITY 


VOL.  II 
PROCESSES  OF  INSTRUCTION 


ffork 

THE   MACMILLAN   COMPANY 
1916 

AU  rights  reserved 


95361 


COPYRIGHT,  1908, 
BY  THE  MACMILLAN  COMPANY. 


Set  up  and  clectrotyped.     Published  April,  1908.     Reprinted 
September,  1909;  October,  1913;  February,  1915;  April,  1916. 


J.  8.  Cashing  Co.  —  Berwick  &  Smith  Co. 
Norwood,  Mass.,  U.S.A. 


0 


7 


PREFACE 

IT  is  to  the  New  Method  of  Bacon,  refined,  corrected, 
and  supplemented  by  the  older  method  first  fully 
described  by  Aristotle,  that  the  world  owes  its  present 
condition  and  rate  of  progress.  By  whatever  path  he 
may  prefer,  the  teacher  must  go  back  to  these  primal 
sources  of  thought  and  efficiency  for  his  teaching 
models,  because  there  are  no  others.  This  volume 
seeks  in  due  measure  to  accomplish  for  the  young 
teacher  what  Mill  and  Jevons  and  Mach  have  done  for 
the  man  of  science ;  namely,  to  impress  upon  him  the 
few  but  vital  mental  processes  that  alone  lead  to  en- 
during results. 

Whatever  function  vicariousness  may  have  to  per- 
form in  the  ethical  world,  it  has  none  whatever  in  that 
of  intellect,  for  in  education  no  man  is  invested  with 
the  right  to  think  for  another;  to  do  so  is  to  negate 
at  once  the  chief  end  for  which  we  educate.  If,  as  we 
are  told,  the  immortal  gods  laugh  with  inextinguishable 
laughter  at  the  follies  of  men,  their  glee  must  indeed 
be  great  when  they  behold  a  teacher  trying  to  educate 
his  students  by  doing  their  thinking  for  them.  But 
perhaps  the  gods  do  not  laugh ;  it  may  be  they  weep. 

Insight  and  efficiency  are  the  two  supreme  results 
to  be  secured  by  our  methods  of  instruction,  for  out  of 


Vi  PREFACE 

insight  grows  what  the  world  calls  culture,  and  out 
of  efficiency,  mental  discipline.  Culture  is  the  total 
refining  effect  —  intellectual,  emotional,  and  volitional 
—  produced  by  insight  into  the  meaning  of  what  is 
learned;  its  quality  depends  upon  the  nature  of  the 
subject-matter,  and  its  quantity  upon  the  scope  and 
intensity  of  the  insight.  Mental  discipline  is  the  in- 
tellectual effect  produced  by  training  in  the  use  of 
what  is  gained  by  insight;  its  quality  depends  upon 
the  nature  of  the  subject-matter,  and  its  quantity  upon 
the  scope  and  intensity  of  the  training.  We  should  not, 
therefore,  try  to  distinguish  between  cultural  and  non- 
cultural  instruction,  for  all  teaching  is  cultural  in 
proportion  to  the  extent  and  quality  of  the  insight  it 
enables  the  student  to  attain.  All  instruction,  likewise, 
is  disciplinary  to  the  extent  that  it  renders  the  student 
efficient  in  the  use  of  what  he  has  learned.  Culture 
and  discipline  are  accordingly  the  inevitable  concomi- 
tants of  all  good  instruction,  and  they  become  in  turn 
the  just  measure  of  its  effectiveness.  To  gain  insight, 
the  student  must  be  incited  to  think ;  to  gain  efficiency, 
he  must  be  stimulated  to  do.  His  practice  must  be 
saturated  with  thought;  his  thought  made  rich  and 
concrete  by  his  practice. 

It  is  the  hope  of  the  author  that  the  study  of  this 
book  will  help  to  render  these  and  other  important 
principles  axiomatic  in  the  mind  of  the  teacher,  so  that 
easily,  naturally,  and  at  last  inevitably,  he  will  instinc- 
tively employ  the  methods  that  lead  to  insight  and 
efficiency;  and  that  ultimately  he  will  become  as  in- 


PREFACE  Vll 

capable  of  using  the  false  in  method  as  the  artist  is 
of  portraying  the  ugly  in  art. 

That  the  use  of  the  book  may  not  invite  to  a  violation 
of  the  very  principles  it  most  insists  upon,  topics  for 
discussion  are  placed  at  the  close  of  the  various  sec- 
tions, to  be  assigned,  perhaps  in  advance,  to  the  mem- 
bers of  the  class  for  recitation  and  report.  The  topics 
assume  an  understanding  of  the  sections  to  which 
they  relate,  and  in  addition  offer  both  student  and 
teacher  opportunity  and  incentive  to  pour  into  them 
all  that  study,  thought,  and  previous  experience  can 
contribute. 

Volume  I  of  this  work  treats  of  The  Studies.  Con- 
trary to  the  original  intention,  it  has  been  deemed  best 
to  restrict  the  present  volume  to  The  Processes  of 
Instruction,  and  to  reserve  for  a  third,  the  remaining 
important  topic  in  the  principles  of  secondary  educa- 
tion, namely,  The  Processes  of  Training. 

The  author  desires  to  express  his  sense  of  obligation 
to  Albert  Anthony  Giesecke,  of  Cornell  University,  for 
his  kindness  in  reading  manuscript  and  proof,  and  to 
Willard  James  Fisher,  of  the  Cornell  Department  of 
Physics,  for  scrutinizing  the  examples  drawn  from  the 
natural  sciences. 

CORNELL  UNIVERSITY, 
April,  1908. 


CONTENTS 

PART   II 

PROCESSES  OF  INSTRUCTION 

A.    SCIENTIFIC  BASIS  FOR  HIGH-SCHOOL 
METHODS 

CHAPTER   I 

THE  ACQUISITION  OF  FACTS 

PACK 

By  Authority 3 

By  Observation 6 

By  Experiment 14 

(1)  The  variable  and  the  variant 15 

(2)  Control  of  the  variable 15 

(3)  Maintenance  of  similarity  of  conditions  .        .  19 

(4)  Collective  experiments 20 

CHAPTER  II 

THE  MEANING  OF  FACTS  — THEIR  EXPLANATION 

The  Problem 21 

The  Means  of  Explanation  —  Hypothesis  and  Analogy      .  28 

(1)  Meaning  and  use  of  the  hypothesis         ...  28 

(2)  First  requisite  for  a  good  hypothesis       ...  32 

(3)  Second  requisite  for  a  good  hypothesis  ...  33 

(4)  The  third  requisite  for  a  good  hypothesis       .         .  34 

(5)  The  experimentum  crucis 37 

(6)  Analogy  as  a  guide  to  discovery     .        .        .        .41 


X  CONTENTS 

CHAPTER   III 

FORMS  OF  SOLUTION  FOR  THE  PROBLEM 

PAGE 

1.  The  Determination  of  Causes  —  Method  of  Agreement 

and  Difference 43 

(1)  The  method  of  agreement      .  .        .         .48 

(2)  The  method  of  difference       .        .         .  -5° 

(3)  The  joint  method  of  agreement  and  difference        .       51 

(4)  The  method  of  concomitant  variations   ...       52 

(5)  The  method  of  residues 53 

2.  Classification '    .       55 

3.  Generalization 60 

(1)  Non-mathematical 60 

(2)  Mathematical 63 

B.     SCIENTIFIC   METHOD   IN   HIGH-SCHOOL 
INSTRUCTION 

CHAPTER   IV 

THE  EDUCATIONAL  STATUS  OF  THE  HIGH-SCHOOL 
STUDENT 

1.  Location  in  the  Field  of  Knowledge 67 

2.  Amount  of  Knowledge  to  be  acquired  —  Nodes  of  Thought      69 

3.  Efficiency  in  the  Use  of  what  is  to  be  Acquired  .         .         .      73 

CHAPTER  V 

THE  INDUCTIVE  APPROACH 

1.  Processes  of  Apperception          .-,.«,        .        .         .      79 

(1)  Setting  the  problem        .        .        .        .        .        .82 

(2)  Acquiring  the  facts 85- 

2.  Processes  of  Thought         .        .        .        .        •        .  91 

(1)  The  hypothesis 93 

(2)  Cause  and  effect 94 

(3)  Classification 96 


CONTENTS  Xi 

PAGE 

(4)  Generalization  in  the  various  studies 

a)  Non-mathematical 99 

b)  Mathematical    .         .        .    '     »        .        .        .108 
3.   Processes  of  Application    .        .        .        .        .        .        .121 

(See  Chapter  VII.) 

CHAPTER  VI 

THE  DEDUCTIVE  APPROACH 

1.  Processes  of  Apperception  in  Deduction  —  Anticipation     .     123 

2.  Processes  of  Thought  —  Use  of  Deduction  to  give  New 

Knowledge  in 

a)  Mathematics 134 

b)  Language 140 

c)  Other  subjects 147 

3.  Processes  of  Application  in  Deduction       ....  149 

(See  Chapter  VII.) 

CHAPTER  VII 

PROCESSES  OF  APPLICATION  IN  INDUCTION  AND 
DEDUCTION 

1.  Need  of  this  Stage  of  High-School  Methods       .        .        .     150 

2.  The  Psychologist  vs.  the  Sociologist  in  Education     .         .152 

3.  The  Laboratory  or  Workshop  Form 155 

4.  Translation  and  Composition  as  Forms  of  Application       .     159 

5.  Application  in  the  Sciences 169 

6.  Application  in  Mathematics 173 

CHAPTER  VIII 
COMBINATIONS  AND  VARIATIONS 

1.  The  Heuristic  Method 178 

2.  Invention  as  a  Mode  of  Thought 182 

3.  Analysis  and  Synthesis 187 

4.  Some  German  Methods 189 


PART   II 

A.    SCIENTIFIC   BASIS   FOR  HIGH-SCHOOL 
METHODS 


CHAPTER  I 

THE  ACQUISITION   OF  FACTS 
i.  By  Authority 

i.  How  does  the  'out-of-school'  world  acquire  its 
facts  ?  Evidently  in  two  ways,  at  first  hand  through  direct 
observation  and  experiment,  and  at  second  hand  through 
authoritative  transmission  by  word  of  mouth  or  by  printed 
page.  Both  methods  are  essential,  since  past  events  are 
not  subject  to  observation,  nor  would  progress  be  possible 
did  not  men  acquire  at  least  some  knowledge  at  first 
hand. 

Courts,  which  deal  largely  with  past  events,  have  their 
rules  of  evidence  whereby  they  hope  to  sift  the  truth  from 
unintentional  error  or  wilful  perjury.  Miinsterberg  sug- 
gests that  courts  should  use  the  methods  of  experimental 
psychology  hi  detecting  false  testimony,  since  for  one 
thing  it  is  found  that  untruthful  answers  to  questions 
occupy  more  time  than  do  truthful  ones.  The  reason 
for  this  is  that  the  witness  involuntarily  takes  at  least 
a  little  additional  time  to  consider  the  probable  bear- 
ings of  what  he  proposes  to  say,  whereas  if  he  be- 
lieves his  evidence  to  be  truthful  throughout,  there  is 

3 


4        SCIENTIFIC    BASIS    FOR    HIGH-SCHOOL    METHODS 

no  need  for  hesitation.1  This,  however,  would  be  test- 
ing evidence  by  experiment. 

Historians,  who  record  and  explain  past  events,  have 
also  their  methods  of  sifting  truth  from  error.  Thus,  there 
are  at  least  half  a  dozen  different  accounts  by  eye-witnesses 
of  the  precise  manner  in  which  Gustavus  Adolphus  met 
his  death  at  the  battle  of  Liitzen.  It  is  only  by  comparing 
these  accounts  with  one  another,  eliminating  inconsisten- 
cies and  absurdities,  and  taking  account  of  inherent  prob- 
abilities that  the  real  facts  can  be  determined  with  any 
considerable  degree  of  certainty. 

The  acquisition  of  facts  at  second  hand  in  the  school, 
however,  constitutes  a  different  problem.  The  authen- 
ticity of  the  facts  themselves  is  not  questioned;  the  need 
of  imparting  them  by  the  authority  of  teacher  or  book 
and  the  manner  of  so  doing  are  the  only  important  ques- 
tions. Occasionally  one  hears  or  reads  the  categorical 
imperative,  "Teach  no  facts  at  second  hand  that  may 
be  acquired  by  the  student  at  first  hand."  Though  the 
motive  of  this  maxim  is  good,  its  effect,  could  it  be  fol- 
lowed, would  be  bad;  for  it  ignores  the  limitations  of  time, 
and  the  magnitude  of  what  is  to  be  acquired  by  the  stu- 
dent in  a  few  years.  He  is  called  upon  to  recapitulate  the 
essentials  of  race  experience  in  every  grand  department  of 
human  and  natural  science,  so  that  even  with  the  best 
of  teaching  he  could  find  out  for  himself  at  first  hand 

1  "The  Third  Degree,"  McClure's,  October,  1907. 


THE    ACQUISITION    OF    FACTS  5 

but  a  fragment  of  what  should  be  acquired.  The  chief 
advantage,  therefore,  of  the  communication  of  facts  by 
authority  is  that  it  saves  time,  thus  enabling  the  student 
to  make  much  more  rapid  progress  than  would  otherwise 
be  possible.  Its  disadvantages  are  obvious  and  pro- 
nounced. In  the  first  place  it  tends  to  beget  a  passive 
attitude  of  mind,  which  leads  to  lack  of  vividness  in  the 
ideas  concerned  and  to  consequent  indifference  toward 
the  subject  itself.  A  second  disadvantage  is  that  where 
the  facts  are  of  vital  importance  because  of  their  weight 
in  determining  causes  or  effects  (classifications  or  gen- 
eralizations), their  rapid  acquisition  often  prevents  full 
recognition  of  their  significance.  A  youth  may  acquire 
the  facts  of  physics  so  rapidly  that  he  fails  to  comprehend 
even  the  simplest  laws  of  the  subject;  he  may  cram  him- 
self so  full  of  the  facts  and  dates  of  history  that  his  mind 
has  neither  time  nor  incentives  to  understand  the  meaning 
of  what  he  has  learned.  The  student  who  thus  stuffs  his 
mind  with  unassimilated  facts  is  like  the  voracious  reader 
of  newspaper  or  novel;  but  he  who  acquires  only  so  fast 
as  he  can  assimilate  resembles  the  investigator,  whose 
new  facts  though  few  are  full  of  meaning. 

The  investigator  takes  his  facts  where  he  can  get  them, 
but  if  they  are  important  for  the  confirmation  or  refutation 
of  theories,  principles,  causes,  or  effects,  he  scrutinizes 
them  carefully  and  where  possible  subjects  them  to  tests 
to  be  sure  that  they  are  true. 


6         SCIENTIFIC    BASIS    FOR    HIGH-SCHOOL    METHODS 

Once,  however,  it  was  sufficient  for  the  acceptance  of 
the  truth  of  an  assertion,  such  as,  "Gravity  causes  heavy 
bodies  to  fall  more  rapidly  than  light  ones,"  that  some  emi- 
nent authority,  like  Aristotle,  had  made  it.  Francis  Bacon 
convinced  the  world  some  three  hundred  years  ago  that 
the  old  custom  of  receiving  material  facts  upon  bare  au- 
thority was  an  unwise  one,  and  he  proposed  a  new  method 
whereby  men  should  test  old  assertions  and  discover  new 
facts  by  direct  observation  and  experiment.  This  method 
is  now  used  in  all  departments  of  human  learning.  Every 
alleged  fact  in  every  field  of  learning  is  now  subject  to 
the  search-light  of  the  investigator.  If  it  cannot  bear  the 
light,  it  is  discarded  as  error. 

2.  By  Observation 

2.  Two  very  obvious  advantages  follow  from  accepting 
Bacon's  method  of  acquiring  and  verifying  facts  by  direct 
observation:  (i)  greater  certainty  that  the  knowledge  thus 
gained  is  true,  and  (2)  the  greater  vividness  with  which  it 
is  impressed  upon  the  mind.  The  latter  advantage  is  of 
particular  importance  to  the  student,  since  he  must 
recapitulate  the  experience  of  the  race  so  rapidly  that  if 
this  vividness  is  lacking,  both  comprehension  and  reten- 
tion are  impaired.  So  patent  are  the  advantages  of  ac- 
quiring knowledge  at  first  hand  by  direct  observation  that 
the  prescription  of  this  method,  especially  in  the  natural 


THE    ACQUISITION    OF    FACTS  7 

sciences,  has  become  a  commonplace  of  modern  literature 
on  education.  The  reception  of  large  masses  of  unques- 
tioned facts  imparted  by  the  method  of  bare  authority 
tends  to  clog  and  deaden  the  mind;  whereas  the  acqui- 
sition of  new  facts  by  observation  arouses  the  curiosity, 
throws  the  mind  into  the  state  of  active  attention,  promotes 
rapidity  of  comprehension,  and  awakens  interest.  The 
best,  perhaps,  of  any  device  known  to  the  schoolmaster, 
it  simulates  the  situations  of  real  life  at  its  best,  and 
thus  arouses  to  activity  a  set  of  powers  that  would  other- 
wise remain  dormant. 

3.  Observation  both  in  and  out  of  the  school  has 
as  a  matter  of  course  an  apperceptive  basis.  What  we  see 
and  how  we  interpret  what  we  perceive  depend  upon  our 
stock  of  knowledge  and  our  prevailing  interests.  One  mind 
may  be  alert  and  curious,  another  dull  and  indifferent,  but 
both  acquire  and  interpret  new  experiences  in  the  light 
of  those  with  which  they  are  most  familiar.  This  leads 
to  what  may  be  called  the  bias  of  apperception.  Huxley 
declares  that  not  one  man  in  a  hundred  will  observe  a 
phenomenon  of  nature  with  accuracy  and  adequacy. 
"So,"  he  remarks,  "we  are  shut  up  to  this  —  that  the 
business  of  education  is,  in  the  first  place,  to  provide  the 
young  with  the  means  and  the  habit  of  observation;  and 
secondly  to  supply  the  subject-matter  of  knowledge  either 
in  the  shape  of  science  or  of  art,  or  of  both  combined."  * 

1  "Science  and  Education,"  p.  175. 


8        SCIENTIFIC    BASIS    FOR    HIGH-SCHOOL    METHODS 

What,  then,  is  the  difference  between  the  observation  that 
is  loose  and  inaccurate  and  that  which  is  precise  and  ade- 
quate? Huxley  says,  again,  "The  man  of  science  simply 
uses  with  scrupulous  exactness  the  methods  which  we  all, 
habitually  and  at  every  moment,  use  carelessly."1  This 
kind  of  observation,  therefore,  rests  upon  adequate  knowl- 
edge, requisite  care,  and  scholarly  or  professional  interest. 
The  difficulty  of  making  discoveries  and  inventions 
shows  that  it  is  one  thing  to  see  and  quite  another  to  per- 
ceive the  relations  of  what  is  observed  to  other  things. 
How  many  times  must  not  the  expansive  power  of  steam 
have  been  observed  before  it  occurred  to  Watt  to  utilize 
its  force !  Earthworms  have  been  observed  in  all  ages, 
but  the  effect  they  have  upon  the  soil  was  not  discovered 
until  recent  times.2  Everybody  has  observed  how  easily 
water  runs  through  sand,  yet  until  the  present  few,  if  any, 
have  thought  to  confine  it  in  the  bottom  of  a  ditch  to  make 
a  drain.  Scientific  observation  is  greatly  assisted  by  care- 
ful record  of  what  is  seen,  for  in  this  there  is  incentive  for 
reflection  and  further  observation.  Thus  Lord  Rayleigh 
and  William  Ramsey 3  in  comparing  the  weight  of  nitro- 
gen derived  from  chemicals  with  that  derived  from  air 
noticed  that  that  which  came  from  air  was  the  heavier. 

1  "  Science  and  Education,"  p.  46. 

2  Darwin,  "Formation  of  Vegetable  Mould  through  the  Action  of 
Worms." 

1  Proceedings  of  the  Royal  Society,  Vol.  57,  pp.  265-287. 


THE    ACQUISITION    OF    FACTS  9 

It  is  related  that  the  fact  was  recorded  with  the  written 
admonition,  "Look  into  this."  At  a  subsequent  time 
they  did  so,  and  discovered  argon,  a  hitherto  unknown 
element  of  the  air.1  This  explains  why  modern  teachers 
of  science  lay  so  much  stress  upon  keeping  a  careful  record 
of  everything  observed.  As  Bain  asserts,  observation  is 
sense  impression  plus  inference.  Without  both  one  can- 
not properly  observe,  but  poor  observation  always  results 
from  an  unjustified  admixture  of  inference  with  sense  im- 
pression. If  we  infer  too  much,  we  think  we  perceive 
what  is  not  true;  if  we  infer  too  little,  we  are  of  those 
who,  "having  eyes,  see  not."  Indolence  in  reflection  or 
preoccupation  may  easily  prevent  the  proper  inference; 
prejudice  or  prepossession  may  induce  a  wrong  one. 
If  we  do  not  know  what  to  look  for  hi  a  given  department 
of  knowledge,  both  facts  and  their  significance  escape  us, 
while  indifference  leads  to  the  same  result. 

DISCUSSION:  —  Examples  of  scientific  observation  among: 
i.  Detectives.  2.  Scholars.  3.  Physicians.  4.  Economists. 
5.  Statesmen.  6.  Primitive  men. 

4.  Observation  rests  primarily  upon  the  unaided  use 
of  the  senses,  but  science  has  devised  a  number  of  instru- 
ments by  which  it  may  be  greatly  extended.  Among  the 
chief  of  these  are  the  following:  telescope,  microscope, 
spectroscope,  dissecting  tools,  coloring  materials,  photo- 

1  Cavendish  in  making  his  analysis  of  the  atmosphere  in  1783  de- 
tected an  unexplained  residuum,  which  is  now  known  to  be  argon. 


10      SCIENTIFIC    BASIS    FOR    HIGH-SCHOOL    METHODS 

graphic  camera,  stereopticon,  balance,  measuring  appa- 
ratus, thermometer,  and  barometer. 

DISCUSSION  :  —  Place  and  function  of  each  of  these  instru- 
mentalities in  high-school  studies. 

5.  Observation,  or  the  gaining  of  knowledge  at  first 
hand,  has  three  essential  stages.  The  first  stage  is  the 
identification  of  objects  by  their  characteristics,  whether 
qualities  or  actions.  By  the  brilliant  crimson  of  this  fallen 
autumn  leaf,  I  know  that  it  came  from  a  maple  tree.  I 
judge  by  the  song  of  yon  distant  warbler  that  it  is  a  thrush. 
The  rustle  in  the  waste-paper  basket  bespeaks  the  mouse. 
The  muffled  creaking  of  the  stairs  at  midnight  intimates 
the  stealthy  approach  of  the  intruder.  We  are  on  the  old 
battle-field  of  Jena.  In  the  distance  rises  a  tapering  object. 
It  is  probably  a  monument.  Nearer  approach  shows  the 
object  to  be  located  in  a  valley.  Now  a  shape  like  a  belfry 
comes  to  view.  It  is  a  church  spire. 

The  second  stage  of  observation  is  the  use  of  our  stored-up 
knowledge  or  experience  to  anticipate  further  observation 
of  characteristics,  in  order  that  the  identification  may  be 
complete.  I  catch  a  glimpse  of  a  fleeting  form  in  the 
bushes.  It  looks  like  a  quail.  If  it  is  a  quail,  it  will  have 
a  rapid,  whirring  flight,  a  plump  brown  form,  and  a  '  Bob- 
White'  whistle.  Going  farther,  I  flush  the  bird,  perceive 
the  form  of  body,  the  manner  of  flight,  and  then  after  a  time 
hear  the  sound  of  his  call.  Now  I  am  sure  of  the  identifica- 
tion. In  the  second  stage  of  observation  it  is  the  class 


THE    ACQUISITION    OF    FACTS  II 

which  suggests  the  additional  characteristics  to  be  looked 
for.  As  soon  as  the  fleeting  glimpse  of  the  running  object 
in  the  hushes  suggested  the  class  quail,  the  well-known 
characteristics  of  this  class  at  once  flashed  into  the  mind, 
and  in  this  way  became  anticipations  of  what  would 
probably  be  found  upon  further  observation.  Should 
the  first  tentative  observation  lead  to  a  wrong  identifica- 
tion, the  anticipations  suggested  by  it  will  not  be  fulfilled. 
Thus,  if  hearing  a  whistle  that  I  think  is  made  by  a  quail, 
I  turn  the  corner  expecting  to  see  the  little  performer  him- 
self, but  find  instead  a  cage  containing  a  mocking-bird 
which  is  mimicking  the  'Bob- White '  call,  my  first  interpre- 
tation is  seen  to  be  erroneous,  and  all  the  anticipations  it 
suggested  are  found  to  be  without  validity.  In  such  cases 
the  mind  instantly  readjusts  its  observations  to  conform 
with  facts. 

The  third  stage  of  observation  is  the  storing  up  of  our 
experience  in  general  terms.  To  illustrate  how  this  occurs, 
the  classification  of  moths  may  be  used.  All  of  us  are  more 
or  less  acquainted  with  them,  how  they  fly  by  night  and 
are  destructive  to  vegetation  and  fabrics.  One  is  named 
the  hawk-moth,  another  the  army-worm  moth,  the  cod- 
ling moth,  etc.  Here  on  the  desk,  however,  is  a  prepara- 
tion of  moths  that  came  from  Germany.  The  wings 
and  bodies  are  variegated  hi  browns  and  yellows,  but  upon 
the  top  of  the  thorax  is  a  curious  marking  in  dark  brown 
and  light  gray  that  reminds  one  of  the  representation  of 


12      SCIENTIFIC    BASIS    FOR    HIGH-SCHOOL    METHODS 

skull  and  cross-bones  used  on  bottles  containing  poison. 
The  label  on  the  preparation  is  as  follows,  Acker ontia 
atropos.  Totenkopf.  It  is  the  death's-head  moth,  of  which 
one  may  read,  but  which  is  never  seen  alive  in  the  United 
States.  There  are  three  of  the  moths  in  this  collection, 
and  we  immediately  assume  that  there  is  a  whole  class  of 
the  creatures  somewhere  in  the  world.  Our  observation 
of  these  new  distinctive  markings  in  an  old  class,  namely, 
moths,  has  therefore  enabled  us  to  form  the  nucleus  for  a 
class  new  to  us,  namely,  death's-head.  In  this  way  our 
observations  become  stored  up  in  new  general  terms,  or 
as  new  elements  in  old  ones. 

Recapitulating,  we  see  that  observation  involves  three 
stages:  first,  the  tentative  identification  of  objects  by 
their  characteristic  qualities  or  actions;  second,  the  use 
of  experience  stored  up  in  our  knowledge  of  classes  to 
anticipate  further  perception  of  characteristics,  in  order 
that  the  first  observation  may  be  verified  and  completed; 
third,  the  storing  up  of  new  experience  in  general  terms. 
It  is  in  this  triple  fashion  that  observation  gives  rise  to 
and  develops  our  knowledge.1 

6.  Much  useful  knowledge  has  been  gained  by  pure 
observation  unaided  by  experiment.  It  was  in  this  way 
probably  that  Aristotle  laid  the  foundations  of  zoology, 
by  describing  some  five  hundred  different  kinds  of  animals, 

1  The  logical  implications  of  this  exposition  are  well  set  forth  in  Dr. 
Win.  T.  Harris's  "  Psychologic  Foundations  of  Education,"  pp.  62-89. 


THE    ACQUISITION    OF    FACTS  13 

collected  for  the  most  part  by  soldiers  in  the  armies  of 
Alexander  the  Great.  It  is  chiefly  by  such  observation 
that  the  great  classifications  in  botany  like  those  of  Linnaeus 
have  been  made,  to  say  nothing  of  the  epoch-making 
labors  of  Darwin,  Wallace,  Bain,  Huxley,  and  the  other 
great  biologists  of  the  nineteenth  century.  The  same  has 
been  true  in  the  domains  of  astronomy,  geology,  anthro- 
pology, ethnology,  and  the  like.  It  is  the  keen  observer 
of  men  and  manners  that  produces  our  novels,  our  social 
essays,  and  our  dramas.  There  are,  however,  many  as- 
pects of  nature  in  which  observation  alone  even  when 
aided  by  scientific  instruments  does  not  enable  us  to  discover 
facts  and  their  relations ;  as,  for  instance,  what  force  gravity 
exerts  at  different  distances,  the  cause  of  yellow  fever, 
the  function  of  nitrogen  in  plant  life.  The  reason  for  this 
inadequacy  of  observation  is  that  the  phenomena  in  ques- 
tion are  so  complicated  with  others  that  the  observer  is 
unable  to  separate  the  real  from  the  seeming.  Thus,  the 
mosquito  has  been  suspected  for  two  thousand  years  of 
having  an  office  in  the  transmission  of  disease,  but  this 
suspicion  has  been  verified  only  in  very  recent  times.  The 
device  which  men  have  hit  upon  to  overcome  this  inade- 
quacy of  direct  observation  is  to  vary  phenomena  under 
controllable  circumstances.  Such  variation  under  control 
is  called  experiment. 


14      SCIENTIFIC    BASIS    FOR    HIGH- SCHOOL    METHODS 

3.  By  Experiment 

7.  Huxley  calls  experiment  artificial  observation.  By 
this  he  means  that  it  is  a  variation  of  phenomena  under 
controllable  circumstances  in  order  to  aid  observation. 
The  first  purpose  of  an  experiment  is  to  enable  the 
experimenter  to  determine  some  fact,  truth,  principle, 
cause,  or  effect;  as,  for  instance,  whether  there  is  any 
difference  in  the  force  of  gravity  exerted  at  the  top  of 
St.  Paul's  Cathedral  and  at  its  foot;1  what  is  the  effect 
of  heat  upon  the  red  precipitate  of  mercury  ?  is  there  poison 
in  the  stomach  of  this  corpse,  or  indication  of  rabies  in  the 
brain  of  this  dog  ?  does  a  culture  from  the  throat  indicate 
diphtheria  ?  are  there  typhoid  germs  in  the  water  supply  ? 
are  there  malarial  bacteria  in  the  blood  of  this  patient? 
has  this  animal  tuberculosis  ?  what  effect  upon  the  expan- 
sion or  contraction  of  metals  has  heat  ?  cold  ?  or,  again, 
what  is  the  effect  of  indiscriminate  charity  upon  the 
tramp  nuisance  ?  what  is  the  effect  of  publicity  upon  cor- 
porate mismanagement? 

The  second  purpose  of  the  experiment  is  to  determine 
quantity ;  as,  for  example,  to  determine  by  means  of  the 
balance  the  exact  quantity  of  each  element  in  a  compound; 
to  measure  the  amount  of  heat,  moisture,  carbon  dioxide, 
ozone,  salt,  or  argon  in  the  atmosphere ;  to  learn  how  much 
power-producing  gas  goes  to  waste  in  smelting  furnaces, 

1  Investigated  by  Hooke. 


THE    ACQUISITION    OF    FACTS  1 5 

in  coke  ovens;  the  per  cent,  of  energy  utilized  in  gas-en- 
gines, in  steam-engines;  how  rapidly  a  falling  body  is 
accelerated  by  gravity.  The  so-called  exact  sciences  are 
especially  benefited  by  quantitative  experiment,  and  the 
social,  political,  and  inexact  natural  sciences  by  the  first 
or  qualitative  experiment. 

DISCUSSION  :  —  Character  of  the  experiments  possible  in 
the  various  high-school  studies. 

8.  So  important  is  the  experiment  as  a  means  for 
acquiring  knowledge  that  it  warrants  a  somewhat  detailed 
exposition. 

(i)   The  Variable  and  the  Variant 

Experiment  as  an  artificial  aid  to  observation  involves 
the  idea  of  a  variable  and  a  variant.  The  variable  is  the 
element  that  we  change  at  will,  while  the  variant  is  the 
corresponding  effect.  Thus,  when  we  apply  changing 
amounts  of  heat  to  a  metal  rod  and  notice  that  for  each 
increase  in  temperature  there  is  an  increase  in  the  length 
of  the  rod,  heat  is  the  variable  and  expansion  the  variant. 
When  we  compress  air  to  see  how  much  heat  is  generated, 
dimension  is  the  variable  and  heat  the  variant. 

(2)   Control  of  the  Variable 

An  experiment  would  be  lacking  in  accuracy  if  the 
variable,  i.e.,  the  element  that  is  changed  at  will,  were  not 


1 6      SCIENTIFIC    BASIS    FOR    HIGH-SCHOOL    METHODS 

under  the  control  of  the  experimenter,  for  otherwise  exact 
repetition  by  any  person  at  any  time  would  not  be  pos- 
sible. Thus,  to  test  the  power  of  windmills  by  fitful  and 
uncontrollable  breezes  would  be  difficult,  but  by  placing 
the  windmills  at  the  end  of  a  bar  revolving  at  known  rates, 
the  variable  is  perfectly  under  control.  Men  do  not  like 
to  wait  until  steamships  are  built  to  find  out  how  fast 
they  can  go,  but  first  make  models  of  the  ships  and  test 
them  in  tanks  of  water.  The  change  in  rate  of  speed  is 
the  variable,  while  the  corresponding  resistance  of  the  water 
is  the  variant. 

By  similar  methods  the  efficiency  of  gas  and  steam- 
engines  may  be  determined,  the  variable  element  being 
always  under  control. 

Sometimes  men  attempt  to  control  the  variable  when 
nature  does  it  better.  As  an  illustration  Galileo's  scheme 
for  determining  the  velocity  of  light  may  be  chosen.  He 
proposed  that  two  men,  A  and  B,  with  dark  lanterns,  should 
be  stationed  at  points  a  considerable  distance  apart.  A 
was  first  to  flash  the  light  from  his  lantern;  then  B  was 
to  open  his  as  soon  as  he  saw  A's  light,  while  A  was  to 
count  the  seconds  that  elapsed  from  the  time  he  opened 
his  own  lantern  until  he  saw  the  light  from  B's.  This 
would  be  the  measure  of  the  time  it  took  the  light  to  go 
from  A  to  B  and  back  again. 

This  experiment  could  not  succeed,  for,  as  we  now 
know,  light  travels  18,600  miles  in  a  tenth  of  a  second, 


THE    ACQUISITION    OF    FACTS 


a  much  less  time  than  it  would  take  A  and  B  to  open 
and  close  the  shutters.  The  variable  in  this  case  defies 
control.  But  Galileo  made  a  telescope  with  which  he 
discovered  the  moons  of  Jupiter.  This  fact  enabled 
another  man,  Olaf  Romer,  to  measure  the  velocity  of 
light  by  watching  Jupiter's  moons.  This  time  nature 
controlled  the  variable  for  him,  though  it  took  half  a  year 
to  complete  the  observation. 

Jupiter  is  483,000,000  miles  from  the  earth,  and  takes 
eleven    and   three-quarter   years    to    complete    a  revo- 


lution about  the  sun;  therefore  it  moves  but  slowly 
through  its  orbit.  By  observing  any  one  of  Jupiter's 
moons,  Romer  determined  the  period  of  its  revolu- 
tion about  the  mother  planet.  But,  perhaps  to  his  sur- 
prise, the  times  of  revolution  varied  at  different  times  of 


1 8      SCIENTIFIC    BASIS    FOR    HIGH-SCHOOL    METHODS 

our  year.  They  were  shortest  when  the  earth  was  near- 
est Jupiter  and  longest  when  farthest  from  it.  In  the 
figure  let  the  dotted  line  AB  represent  a  section  of  the 
orbit  of  Jupiter;  let  J  represent  Jupiter  with  its  shadow 
and  M  one  of  its  moons.  E1  is  the  earth  when  nearest 
Jupiter,  and  E2  when  farthest  from  it,  six  months  later. 
S  is  the  sun.  The  period  that  elapses  from  one  disappear- 
ance of  Jupiter's  moon  in  the  shadow  until  the  next  is 
the  time  of  its  revolution.  As  the  earth  moves  around  its 
orbit  toward  E2,  the  time  of  revolution  of  Jupiter's  moon 
seems  to  lengthen,  until  when  the  earth  reaches  E2  it  is 
i6|  minutes  longer  than  when  at  Ej.  On  the  other  hand, 
as  the  earth  again  approaches  its  position  at  Elt  the  time 
of  revolution  correspondingly  shortens.  Romer  at  once 
surmised  that  this  variation  was  not  due  to  any  irregularity 
in  the  revolution  of  Jupiter's  moon,  but  to  the  additional 
time  necessary  for  the  light  coming  from  the  satellite  to 
traverse  the  distance  from  JEj  to  Ez.  Knowing  the  distance 
across  the  earth's  orbit  from  E1  to  E2,  he  had  but  to  divide 
this  by  i6£  to  find  how  far  light  travels  in  a  minute,  and 
this  result  by  60  to  know  how  far  it  goes  in  a  second,  or 
186,000  miles. 

As  Mach1  observes,  this  method  is  exactly  that  of 
Galileo,  except  that  the  conditions  are  better  and  nature 
controls  the  variable,  namely,  the  varying  distances  at 

'Compare  Ernst  Mach,  "Popular  Scientific  Lectures,"  translation, 
Open  Court  Publishing  Co.,  Chicago,  1895. 


THE    ACQUISITION    OF    FACTS  19 

which  the  observations  are  taken,  while  Jupiter's  shadow 
furnishes  the  one  dark  lantern  necessary  for  the  experiment. 
It  was  in  1675-1676  that  Romer,  for  the  first  time  in  the 
history  of  the  world,  measured  in  this  manner  the  velocity 
of  light.  Now  by  means  of  perforated  revolving  disks  any 
well-equipped  laboratory  can  perform  the  experiment  pro- 
posed by  Galileo  within  the  limits  of  the  laboratory,  since 
men  have  learned  how  to  control  the  variable. 

DISCUSSION  :  —  Show  how  the  variable  is  controlled  in 
an  experiment  in:  i.  Physics.  2.  Chemistry.  3.  On  men- 
tal effects  of  fatigue.  4.  On  the  effect  of  omitting  number 
work  from  the  first  two  grades. 

(3)  Maintenance  of  Similarity  of  Conditions 

Unless  conditions  are  kept  similar  throughout  an  experi- 
ment or  a  series  of  experiments,  the  results  will  not  be  con- 
clusive. Thus,  when  Newton  proposed  to  test  by  the  use 
of  the  pendulum  the  effect  of  gravity  upon  substances  of 
equal  weight  but  of  different  constitution,  say  a  pound 
of  lead  and  a  pound  of  feathers,  he  arranged  a  set  of  uni- 
form cylindrical  boxes  to  be  suspended  from  pendulums. 
In  these  boxes  he  could  place  equal  weights  of  the  various 
substances  and  learn  by  the  periods  of  vibration  whether 
before  the  court  of  gravity  a  pound  of  feathers  is  the  equiva- 
lent of  a  pound  of  lead. 

Joule's1  experiment  to  show  that  changes  in  the  intrinsic 
energy  of  a  gas  are  manifest  as  changes  hi  temperature, 

1  James  Prescott  Joule,  English  physicist,  1818-1889. 


20      SCIENTIFIC     BASIS    FOR    HIGH-SCHOOL    METHODS 

derives  much  of  its  convincing  force  by  the  maintenance  of 
similarity  of  conditions.  He  took  two  vessels,  one  empty 
and  the  other  filled  with  gas  at  a  high  pressure,  connected 
them  with  a  stop-cock,  and  submerged  both  in  a  third 
vessel  rilled  with  water.  Then  he  opened  the  stop-cock 
and  observed  the  results.  The  water  in  which  the  two 
vessels  were  submerged  did  not  change  its  temperature, 
thus  showing  that  a  gas  expanding  into  a  vacuum,  and  so 
doing  no  work,  neither  warms  nor  cools  its  surroundings, 
within  the  limits  of  error  of  observation. 

DISCUSSION  :  —  Efforts  made  to  preserve  similarity  of  con- 
ditions in  agricultural  experiment  stations ;  in  testing  the  men- 
tal effects  of  fatigue  in  school  children. 

(4)   Collective  Experiments 

Many  experiments  admit  of  a  collective  or  cumulative 
result,  as  may  be  illustrated  by  the  use  of  sand  upon  a 
vibrating  metal  plate  to  show  where  the  centres  of  vibra- 
tion and  of  relative  quiescence  are.  In  a  similar  manner, 
iron  filings  may  be  used  to  reveal  to  the  eye  lines  of  electric 
force.  Melting  wax  upon  heated  crystals  will  show  whether 
the  heat  applied  is  conducted  uniformly  or  not.  The 
parabolic  path  of  a  jet  of  water  under  pressure  intimates 
to  sight  what  the  path  of  a  projectile  will  be.  The  motions 
of  invisible  gases  may  be  rendered  visible  by  producing 
within  them  a  cloud,  such  as  is  made  by  smoke,  dust, 
fumes,  etc. 


CHAPTER   H 

THE  MEANING  OF  FACTS  —  THEIR 
EXPLANATION 

i.  The  Problem 

9.  The  term  problem  is  used  in  two  senses :  (i)  a  task  or 
exercise  set  for  the  application  of  rules  or  principles  already 
established,  as  a  problem  in  mathematics;  (2)  something 
to  be  investigated,  that  causes  or  effects  may  be  discovered, 
classifications  established,  or  generalizations  derived;  as, 
what  is  the  cause  of  dew  ?  according  to  what  law  is  light 
diffused  ?  in  what  class  does  the  amphioxus  belong  ?  The 
outside  world  is,  of  course,  interested  only  in  problems  of 
the  second  kind. 

A  problem  hi  the  second  sense  arises  when  there  is  in- 
congruence  between  facts  and  thoughts,  whereas  stable 
customary  relations  between  facts  and  ideas  give  rise  to 
few  problems.  When  it  is  asked,  Why  does  iron  rust? 
the  fact  of  rusting  is  apparent,  but  the  reason  may  be  un- 
known. In  this  case  a  problem  arises.  In  the  words  of 
Mach :  "  The  Child  just  awakening  into  consciousness  of 
the  world  knows  no  problems.  The  bright  flower,  the 
ringing  bell,  are  new  to  it;  yet  it  is  surprised  at  nothing. 

21 


22      SCIENTIFIC    BASIS    FOR    HIGH- SCHOOL    METHODS 

The  out  and  out  Philistine,  whose  only  thoughts  lie  in 
the  beaten  path  of  his  everyday  pursuits,  likewise  has  no 
problems.  Everything  goes  its  wonted  course,  and  if  per- 
chance a  thing  go  wrong  at  times,  it  is  at  most  a  mere 
object  of  curiosity  and  not  worth  serious  consideration. 
In  fact,  the  question  'Why?'  loses  all  warrant  in  relations 
where  we  are  familiar  with  every  aspect  of  events.  But 
the  capable  and  talented  young  man  has  his  head  full  of 
problems ;  he  has  acquired  to  a  greater  or  less  degree  cer- 
tain habitudes  of  thought,  and  at  the  same  time  he  is 
constantly  observing  new  and  unwonted  facts,  and  in  his 
case  there  is  no  end  to  the  question  'Why?'"  * 

Some  problems  are  of  perpetual  interest,  as,  What  is 
the  origin  of  evil  ?  Was  Hamlet's  insanity  real  or  feigned  ? 
Many  arise  from  new  wants  or  newly  perceived  incongru- 
ences,  as,  How  can  live  fish  be  transported  long  distances 
without  water  ? 2  How  restore  the  lost  inscription  upon 
the  Parthenon  from  the  nail  holes  where  the  letters  were 
fastened  to  the  stone  ? 3  Again,  thoughts  which  may  be 
old  and  familiar  frequently  come  into  new  relations,  and 
thus  give  rise  to  problems.  The  effort  to  establish  a  rela- 
tion of  which  we  have  merely  heard  gives  rise  to  a  problem. 
Galileo,  for  illustration,  heard  of  an  invention  in  Holland 
which  made  distant  objects  seem  near.  At  the  first 

1  Ernst  Mach,  "Popular  Scientific  Lectures,"  p.  223. 
1  See  section  86. 

3  See  account  by  E.  P.  Andrews,  who  accomplished  this  feat.  Ce«- 
tury,  June,  1896. 


THE    MEANING    OF    FACTS  —  THEIR    EXPLANATION     23 

opportunity  in  Padua  he  made  a  telescope  from  a  lead 
organ-pipe  and  two  lenses.  Six  days  later  he  produced  a 
much  more  perfect  instrument  in  Venice.  He  knew  about 
lenses  before,  but  had  never  thought  of  them  in  such  rela- 
tion as  to  constitute  a  telescope  until  he  read  of  the  dis- 
covery in  Holland. 

10.  Invention  may  be  regarded  as  a  special  case  of 
problem-solving,  the  only  difference  being  that  the  end  of 
invention  is  technical  and  practical,  whereas  the  problem 
as  such  is  more  theoretical.    Modern  technical  advance 
is  due  largely  to  the  fact  that  the  form  of  problem-solving 
known  as  invention  is  no  longer  fortuitous,  resting  upon 
primitive  conceptions,  but  is  systematically  pursued  by 
men  having  thorough  scientific  knowledge,  and  employed 
for  the  most  part  by  industrial  corporations.     Similarly, 
social  and  economic  problems  are  attacked  by  men  of 
resolution  and  insight,  as  seen  in  such  cases  as  the  meth- 
ods of  philanthropy,  the  race  problem,  cooperative  house- 
keeping,  control  of  corporations,  international  arbitra- 
tion, intensive  farming,  etc. 

DISCUSSION  :  —  Compare  modern  inventions  in  automo- 
biles with  the  primitive  invention  of  the  wheel;  smokeless 
powder  with  common  gunpowder;  the  small  caliber,  high 
power  rifle  with  the  matchlock. 

11.  The  problem  is  well-nigh  universal  in  every  field 
of  endeavor,  educational  and   vocational,  for  whenever 
the  adjustment  of  thought  to  fact  or  of  fact  to  thought 


24      SCIENTIFIC    BASIS    FOR    HIGH-SCHOOL    METHODS 

is  involved,  there  the  problem  lies  close  at  hand.  That 
it  is  of  supreme  educational  importance  in  the  sciences 
cannot  be  doubted;  it  is  equally  serviceable  in  the  human- 
ities whenever  the  student  should  be  incited  to  think. 
History  easily  resolves  itself  into  a  series  of  problems 
respecting  cause  and  effect.  Every  literary  masterpiece 
fairly  bristles  with  problems  psychological,  social,  ethical, 
and  linguistic.  Even  the  purely  aesthetic,  whose  appre- 
ciation is  usually  considered  to  rest  upon  contemplation 
alone,  is  greatly  aided  by  intellectual  comprehension,  which 
always  permits  the  problem  form.  The  difference  between 
the  aesthetic  appreciation  of  the  connoisseur  and  that  of 
the  rustic  is  explained  by  this  fact. 

DISCUSSION  :  —  Examples  of  how  subject-matter  falls  into 
the  problem  form  in  science,  in  history,  in  literature,  in  art, 
in  ethics,  in  psychology,  in  economics,  in  politics. 

12.  Problems  are  of  all  degrees  of  magnitude  and  of 
importance.  Professor  Droysen  lectures  for  a  semester 
at  Halle  to  solve  the  problem  why  Gustavus  Adolphus 
of  Sweden  intervened  in  the  German  Thirty  Years'  War, 
and  finds  that  he  did  so  primarily  from  political  rather  than 
from  religious  motives.  John  Fiske  raises  but  does  not 
seriously  try  to  solve  the  problem  as  to  why  the  Confed- 
erate army  was  not  more  vigorously  pursued  at  the  close 
of  the  second  day  at  Shiloh.  After  making  a  few  surmises, 
he  closes  by  quoting  General  Sherman's  reply  when  this 


THE    MEANING    OF    FACTS  —  THEIR    EXPLANATION     25 

question  was  asked:  "I  assure  you,  my  dear  fellow,  we 
had  had  quite  enough  of  their  society  for  two  whole  days, 
and  were  only  too  glad  to  be  rid  of  them  on  any  terms !" 
Students  may  now  be  led  to  solve  problems  in  a  day  or 
a  week  that  were  originally  the  work  of  years  or  of  gen- 
erations. Of  such  nature  are  the  problems  of  combustion, 
the  formation  of  dew,  the  vibratory  propagation  of  light, 
the  velocity  of  light,  the  diffusion  of  light,  the  laws  of 
electricity,  the  origin  of  species,  the  function  of  the  cell 
in  plant  and  animal  life.  It  will  be  seen  later  in  detail 
that  whenever  the  nature  of  a  lesson  is  such  as  to  invite 
or  challenge  thoughtful  investigation,  it  may  fall  into  the 
problem  form.  The  form  of  assignment  is  limited  chiefly 
by  the  amount  of  time  at  the  command  of  student  and 
teacher.  This  is  a  part  of  the  larger  question  as  to  which 
method  of  acquiring  knowledge  is  to  be  preferred  in  any 
given  case,  —  transmission  by  authority  or  first-hand  obser- 
vation. Where  the  latter  method  is  in  place,  to  ask  for 
the  determination  of  cause  or  effect,  of  law,  principle,  or 
classification,  is  by  implication  to  use  the  problem  form. 
A  general  problem  often  gives  rise  to  a  number  of  minor 
problems.  Thus  in  finding  out  the  cause  of  rust  in  iron 
filings,  a  minor  problem  arises  when  we  try  to  discover 
whether  any  of  the  oxygen  active  in  the  rusting  process 
comes  from  the  water  in  which  the  filings  were  immersed. 
This  question  is  answered  by  testing  for  free  hydrogen, 
since  we  know  that  the  component  parts  of  water  are 


26      SCIENTIFIC    BASIS    FOR    HIGH-SCHOOL    METHODS 

oxygen  and  hydrogen.    In  such  cases,  the  minor  problems 
are  steps  in  the  solution  of  the  major  ones. 

DISCUSSION  :  —  Distinguish  between  major  and  minor 
problems  in  each  department  of  learning.1 

13.  Some  of  the  problems  of  the  modern  world  are  a 
standing  challenge  to  the  intelligence  and  enterprise  of 
men;  others  are  of  a  progressive  nature  wherein  each  prob- 
lem solved  is  the  last  step  of  a  series,  and,  in  turn,  sug- 
gests new  ends  to  be  reached.  To  the  first  class  belong 
such  problems  as  these:  How  convert  the  force  daily 
expended  in  the  tides  into  useful  work?  How  utilize  the 
dynamic  power  of  sunshine  to  help  do  the  work  of  the 
world?  How  overcome  diseases  hitherto  incurable? 
How  banish  poverty,  drunkenness,  and  crime  from  the 
world  ?  How  make  the  atmosphere  give  up  enough  of  its 
nitrogen  to  fertilize  the  earth  ?  How  develop  in  a  child 
all  his  latent  possibilities  for  good?  We  have  on  every 
side  examples  of  that  serial  arrangement  of  problems  and 
their  solution  which  leads  to  development.  Beginning 
with  the  simple  curved  sickle  of  the  days  of  Ruth,  we  have  a 
series  of  solutions  to  the  problem  of  rapid  and  economical 
reaping  of  grain,  as  follows:  the  sickle;  the  scythe;  the 
cradle;  the  McCormick  reaping  machine,  first  with  a 
platform  for  hand  raking  into  bundles,  then  perfected  as 

1  For  a  modern  discussion  of  the  major  problems  in  each  domain  of 
knowledge,  see  the  proceedings  of  the  Congress  of  Arts  and  Science,  St 
Louis  Exposition,  Houghton,  Minim  &  Co.,  Boston. 


THE    MEANING    OF    FACTS  —  THEIR    EXPLANATION     2f 

a  self -raker;  then  the  Marsh  harvester,  so  arranged  that 
two  men  could  ride  on  the  machine  and  do  all  the  binding; 
and  finally  the  self-binder  on  the  one  hand  and  the  header 
with  thrashing  machine  attached  on  the  other.  A  similar 
progression  can  be  traced  in  the  development  of  the  rail- 
road. First  we  have  cars  drawn  by  horses  and  running 
on  wooden  rails,  to  be  followed  soon  by  trains  of  old- 
fashioned  stage-coaches  drawn  by  a  crude  steam-engine. 
Some  of  the  important  steps  of  the  progress  are  as  follows: 
placing  the  exhaust  pipe  in  the  smoke-stack,  thus  producing 
a  draft  proportional  to  the  amount  of  power  exerted;  in- 
venting the  swiveling  truck,  enabling  the  train  to  run 
safely  on  a  curved  track;  devising  and  perfecting  the  air- 
brake, enabling  the  engineer  to  manage  successfully  very 
heavy  trains;  converting  crude  molten  iron  into  steel  by 
the  Bessemer  method,  and  the  corresponding  series  of  in- 
ventions which  have  culminated  in  our  great  rolling  mills, 
that  rails  strong  enough  to  support  these  mighty  locomo- 
tives and  their  long  trains  of  heavy  cars  might  be  made. 
To  trace  the  evolution  of  all  these  serial  problems  would 
constitute  in  itself  no  mean  education. 

DISCUSSION:  —  Similar  illustrations:  i.  In  machinery 
for  making  cloth.  2.  In  printing.  3.  In  applying  electricity. 
4.  In  the  perfection  of  automobiles.  5.  Steam  and  water 
turbines.  6.  In  caring  for  criminal  classes.  7.  In  educat- 
ing defectives.  8.  In  making  cities  sanitary.  9.  In  pho- 
tography. 10.  In  the  development  of  musical  instruments. 


28      SCIENTIFIC    BASIS    FOR    HIGH-SCHOOL    METHODS 

2.  The  Means  of  Explanation  —  Hypothesis  and  Analogy 

14.  Authority  and  observation  supplemented  by  ex- 
periment give  us  facts.    The  problem  shows  us  where  to 
search  for  their  meaning;  while  hypothesis  and  analogy 
guide  us  in  the  search.     "If  the  Almighty  were  in  one 
hand  to  offer  me  truth,  and  in  the  other  the  search  after 
truth,  I  would  humbly  but  firmly  choose  the  search  after 
truth."  1 

"I  am  convinced  that  the  method  of  teaching  which 
approaches  most  nearly  the  methods  of  investigation  is 
incomparably  the  best ;  since  not  content  with  serving  up 
a  few  barren  and  lifeless  truths,  it  leads  to  the  stock  on 
which  they  grew;  it  tends  to  set  the  learner  himself  on 
the  track  of  invention  and  to  direct  him  into  those  paths 
in  which  the  author  has  made  his  own  discoveries."2 

(i)  Meaning  and  Use  of  the  Hypothesis 

15.  "When  facts  are  already  in  our  possession  we  frame 
an  hypothesis  to  explain  their  mutual  relations,  and  by  the 
success  or  non-success  of  this  explanation  is  the  value  of 
the  hypothesis  to  be  entirely  judged."  8    For  illustration, 
let  the  problem  be,  What  causes  iron  to  rust?    In  order 
to  find  a  clew  to  the  solution,  the  first  hypothesis  may  be 
this :  Since  the  iron  changes,  it  is  probable  that  its  weight 
before  and  after  rusting  is  different.    This  surmise  may 

1  Lessing.  *  Burke. 

1  William  Stanley  Jevons,  "  Principles  of  Science,"  p.  504. 


THE    MEANING    OF    FACTS  —  THEIR    EXPLANATION     2Q 

be  tested  first  by  weighing  a  quantity  of  unrusted  iron 
filings,  and  then,  after  keeping  the  same  filings  moist  for 
a  few  days,  by  weighing  them  again.  It  is  found  that  the 
weight  has  increased.  The  problem  now  becomes,  What 
is  the  source  of  the  increased  weight  ?  A  little  reflection 
shows  that  the  filings  have  been  exposed  both  to  air  and 
to  water.  A  natural  hypothesis  would  be  that  the  increase 
comes  either  from  the  air  or  the  water,  or  perhaps  both. 
To  see  if  the  air  has  contributed  to  the  increased  weight, 
suspend  a  bag  of  bright  filings  in  a  pot  of  water  and  in- 
vert a  glass  jar  over  the  bag.  It  is  found  that  the  water 
gradually  rises  in  the  jar  until  it  fills  one-fifth  of  the  space 
formerly  occupied  by  the  air.  This  shows  that  the  air 
has  much  to  do  with  the  rusting,  for  it  has  evidently  given 
up  one-fifth  of  its  volume  while  the  filings  were  rusting. 
Further  tests  will  show  that  it  is  oxygen  that  has  been 
given  up  by  the  air,  since  what  is  left  in  the  jar  will  not  sup- 
port combustion.  Then  comes  the  query,  Did  the  water 
also  contribute  oxygen  ?  This  may  be  answered  by  testing 
the  contents  of  the  inverted  jar  for  hydrogen,  for  it  is  known 
that  water  is  composed  of  the  two  gases,  oxygen  and  hydro- 
gen, so  that  if  the  water  has  given  up  to  the  filings  any 
portion  of  its  oxygen,  there  must  be  left  a  corresponding 
portion  of  hydrogen  gas,  which  being  even  lighter  than 
air  will,  of  course,  rise  to  the  top  of  the  inverted  jar. 

New  problems  concerning  combustion,  and  the  consti- 
tution of  air  and  water,  naturally  arise  from  this  investiga- 


30      SCIENTIFIC    BASIS    FOR    HIGH- SCHOOL    METHODS 

tion  of  the  cause  of  rusting,  when,  of  course,  new  hypothe- 
ses are  needed.  Just  what  these  problems  and  hypothe- 
ses shall  be,  will  depend  upon  the  state  of  the  student's 
knowledge  of  chemistry.  What  is  a  known  fact  or  law 
to  one  may  be  a  problem  to  another. 

1 6.  The  hypothesis  in  the  scientific  sense  is  merely  a 
tentative  assumption,  still  to  be  proved,  that  contributes 
to  an  easier  understanding  of  the  facts.1  It  need  not  be 
true  in  order  to  be  useful.  The  essential  thing  is  that  it 
should  be  put  to  the  test,  for  in  this  way  its  adequacy  or 
inadequacy  will  be  revealed.  Even  if  the  hypothesis 
should  turn  out  to  be  entirely  erroneous,  the  test  is  likely 
to  suggest  a  better  one.  In  the  words  of  Priestley: 
"  Very  lame  and  imperfect  theories  are  sufficient  to  suggest 
useful  experiments,  which  serve  to  correct  these  theories, 
and  give  birth  to  others  more  perfect.  These,  then, 
occasion  further  experiments,  which  bring  us  still  nearer 
to  the  truth."2 

In  reality,  the  hypothesis  as  above  considered  is  noth- 
ing but  a  refinement  of  our  instinctive  reaching  forward  to 

1  This  it  will  be  seen  is  the  reverse  of  the  geometrical  use  of  the  term 
hypothesis  as  the  sum  of  conditions  under  which  a  proposition  holds 
and  can  be  demonstrated.  Here  the  hypothesis  is  that  which  is  given  to 
which  no  other  condition  except  mathematical  and  logical  possibility  is 
attached.  We  proceed  from  the  geometrical  hypothesis  to  the  proof  of 
the  proposition.  Other  sciences  reverse  this  process,  beginning  with  the 
given  facts  to  prove  the  hypothesis  true  or  false. 

1 "  History  and  Present  State  of  Discoveries  Relating  to  Vision,  Light, 
and  Colors."  London,  1772.  Vol.  I,  p.  181. 


THE    MEANING    OF    FACTS  —  THEIR    EXPLANATION     31 

surmise  the  causes  or  effects  of  uncomprehended  phe- 
nomena that  attract  our  attention.  Columbus  sees  in  the 
floating  ddbris  of  the  ocean  signs  of  land,  and  at  once  sur- 
mises that  they  are  evidences  of  the  land  he  is  seeking. 
Primitive  men  explain  lightning,  thunder,  hurricanes,  and 
earthquakes  as  the  work  of  titans  or  demons.  For  nearly 
fourteen  centuries  civilized  men  explained  the  apparent 
movements  of  the  heavens  as  the  result  of  different  celes- 
tial spheres  revolving  at  different  rates  about  the  earth,  and 
thus  developed  the  Ptolemaic  astronomical  hypothesis, 
which  was  finally  displaced  by  that  of  Copernicus.  Need- 
less to  say  the  hypothesis  of  Copernicus  has  long  been  a 
demonstrated  truth.  Mach  *  relates  that  when  the  skele- 
tons of  mammoths  were  unearthed  in  Siberia,  the  natives 
explained  them  as  being  the  remains  of  gigantic  rats, 
which  burrowed  in  the  earth,  but  died  as  soon  as  they 
reached  the  air.  This  instinctive  attempt  to  explain 
things  by  means  of  hypothesis  is  akin  to  the  'anticipa- 
tions of  perceptions'  already  explained.2  When  Francis 
Parkman  asked  an  old  Indian,  named  Red  Water,  the 
cause  of  thunder,  he  said:  "It  was  great  blackbird;  and 
once  he  had  seen  it  in  a  dream  swooping  down  from  the 
Black  Hills,  with  its  loud  roaring  wings;  and  when  it 
flapped  them  over  a  lake,  they  struck  lightning  from 
the  water."  8 

1  "Erkentniss  und  Irrtum,"  p.  233.  J  See  pp.  10,  u. 

1  John  Fiske,  "A  Century  of  Science,"  p.  241. 


32      SCIENTIFIC    BASIS    FOR    HIGH-SCHOOL    METHODS 

DISCUSSION  :  —  i .  Primitive  hypotheses  regarding  heavenly 
bodies  and  striking  natural  events  (eclipses,  storms,  earth- 
quakes, seasons,  etc.).  See  sun  and  other  nature  myths. 
2.  Examples  of  instinctive  hypothesis  to  explain  uncompre- 
hended  events  in  daily  life  (sickness,  accidents,  misfortunes, 
conduct  of  others,  etc.). 

(2)   First  Requisite  for  a  Good  Hypothesis 

17.  An  hypothesis  to  be  good  should  offer  the  possibility 
for  deductive  reasoning.  In  other  words,  we  should  be 
able  to  learn  what  ought  to  happen  according  to  such 
an  hypothesis.  To  assume  that  thunder,  lightning, 
hurricanes,  earthquakes,  and  eclipses  are  caused  by 
demons,  would  not  be  a  good  hypothesis,  because  nobody 
can  possibly  predict  with  any  certainty  what  capricious 
power  will  do,  or  in  any  way  test  it  by  experiment.  An 
hypothesis  may  have  great  and  even  apparently  insur- 
mountable difficulties  attached  to  it,  and  yet  be  legitimate 
and  useful,  because  of  the  help  it  gives  in  understanding 
phenomena,  and  because  in  important  respects  it  is  veri- 
fiable by  experiment,  as  in  the  undulatory  theory  of  light. 
The  actual  wave  length  of  the  undulations  can  be  measured. 
Even  the  emanation  theory  of  light  did  good  service, 
since  it  helped  to  explain  many  phenomena,  and  especially 
because  it  did  not  involve  the  assumption  of  ether  to  bear 
the  undulations,  say  from  the  sun  to  the  earth.  The  only 
reason  it  is  now  displaced  is  that  the  undulatory  theory 
explains  more  known  facts,  and  because  it  bears  the  test  of 


THE    MEANING    OF    FACTS  —  THEIR    EXPLANATION     33 

certain  crucial  experiments,  which  the  emanation  theory 
does  not.1  Descartes's  theory  that  the  heavenly  bodies 
are  whirled  about  in  vortices  does  not  present  any  mode  of 
calculating  the  exact  relations  between  the  distances  and 
periods  of  the  planets  and  satellites,  hence  fails  to  satisfy 
this  first  requisite  of  a  good  hypothesis.  It  is  not  a  good 
answer  to  the  objection  that  a  given  hypothesis  can  never 
be  proved,  to  say  that  neither  can  it  be  disproved.  The 
hypothesis  that  nature  abhors  a  vacuum  does  not  show 
why  water  will  not  rise  more  than  33  feet  in  a  com- 
mon pump.  The  old  phlogiston  theory  of  combustion 
violated  the  first  requisite,  since  it  furnished  no  compre- 
hensible basis  for  explanation.  It  was,  however,  shown 
to  be  absurd.  The  known  cannot  be  successfully 
explained  by  means  of  the  unknown. 

DISCUSSION: — i.  Meaning  of  the  word  crucible.  What 
inadequate  hypothesis  led  early  chemists  to  put  a  cross  upon 
their  retorts  ?  2.  Origin  of  moon  and  other  superstitions. 

(3)   Second  Requisite  for  a  Good  Hypothesis 

1 8.  An  hypothesis  should  be  consistent  with  the  estab- 
lished laws  of  nature.  No  hypothesis  can  be  considered 
good  which  contradicts  the  established  laws  of  motion,  of 
gravity,  of  the  conservation  of  energy,  or  even  of  well- 
known  human  nature.  The  attempt  so  often  made  by 
boys  and  unscientific  men  to  invent  machines  that  involve 

1  See  William  Stanley  Jevons,  "Principles  of  Science,"  p.  511. 
D 


34      SCIENTIFIC    BASIS    FOR    HIGH- SCHOOL    METHODS 

the  idea  of  perpetual  motion,  that  is,  machines  that  con- 
tinue to  do  work  without  renewing  energy,  is  a  case  in 
point.  A  fruitful  source  of  hypothesis  lacking  in  this 
second  requisite  is  to  assume  that  the  known  laws  of 
one  department  of  knowledge,  say  biology,  hold  with  un- 
diminished  validity  in  another,  say  human  society.  Thus, 
a  writer  may  construct  his  entire  system  on  the  hypothe- 
sis that  laws  which  hold  in  the  animal  world  hold  also 
with  the  same  rigidity  in  the  human  world.  The  so-called 
Malthusian  law  that  population  always  tends  to  press 
against  the  means  of  subsistence  is  an  illustration.  So  much 
more  rapidly  than  population  are  the  means  of  subsistence 
now  increasing,  that  the  Malthusian  law,  once  the  terror 
of  the  moralist,  has  gone  into  a  state  of  suspended  ani- 
mation.1 When  John  Locke  speaks  of  stones  as  growing, 
he  assumes  that  a  law  of  life  applies  in  geology.2 

DISCUSSION: — i.  Test  the  single  tax  theory  by  this  hy- 
pothesis. 2.  The  theory  that  nations  necessarily  rise,  decline, 
and  perish. 

(4)    The  Third  Requisite  for  a  Good  Hypothesis 
19.  An  hypothesis  should  be  in  conformity  with  facts. 
This  is  its  final  test.    Descartes's  theory  of  vortices  was 
shown  to  be  inadequate,  because  the  rotary  motions  of 

1  See  S.  N.  Patten,  "The  New  Basis  of  Civilization,"  also  "The 
Failure  of  Biologic  Sociology,"  in  Annals  of  the  Academy  of  Political 
and  Social  Science. 

7  John  Locke,  Works,  Vol,  III,  p.  294. 


THE    MEANING    OF    FACTS  —  THEIR    EXPLANATION     35 

sun  and  planets  on  their  own  axes  are  in  striking  conflict 
with  the  revolution  of  the  satellites  carried  around  them, 
and  because  comets  pursue  their  courses  irrespective  of 
the  vortices  which  are  supposed  to  be  whirling  much  more 
solid  bodies  in  their  grasp.  The  present  age  is  notable 
not  only  for  its  willingness  to  test  all  hypotheses  upon  the 
touchstone  of  fact,  but  for  its  determination  to  do  so. 
For  illustration,  the  assumption  that  bees  communicate 
with  one  another  by  means  of  antennae  might  once  have 
been  accepted  or  denied  without  actual  test  to  see  whether 
it  accords  with  fact  or  not.  Huber,  however,  divided  a 
hive  into  two  chambers  by  means  of  a  partition.  Great 
excitement  at  once  ensued  in  that  portion  of  the  hive 
where  there  was  no  queen,  and  the  bees  immediately  set  to 
work  to  build  royal  cells  for  the  creation  of  a  new  queen. 
Huber  then  divided  a  hive  in  exactly  the  same  manner, 
with  the  difference  only  that  the  dividing  screen,  or  parti- 
tion, was  made  of  trellis  work,  through  the  openings  of 
which  the  bees  on  either  side  could  pass  their  antennae. 
Under  these  circumstances  the  bees  in  the  queenless  half 
of  the  hive  exhibited  no  disturbance,  nor  did  they  construct 
any  royal  cells,  for  the  bees  in  the  other  half  of  the  hive  were 
able  to  inform  them  that  the  queen  was  safe.1  This  test 
of  fact  is  reliable  as  far  as  it  goes,  but  further  tests  are 
necessary  to  make  the  evidence  conclusive,  for  the  inter- 
stices in  the  partition  would  permit  of  the  passage  of  sound 

1  Compare  George  John  Romaines,  "Mental  Evolution  in  Man,"  p.  90. 


36      SCIENTIFIC    BASIS    FOR    HIGH-SCHOOL    METHODS 

as  well  as  of  antennae,  whereas  the  solid  partition  would 
exclude  both.  The  rival  hypothesis  that  bees  communi- 
cate by  notes  or  tones  may  turn  out  to  be  in  accordance 
with  the  real  facts.  Only  further  tests  could  determine 
which  hypothesis  agrees  with  them.  It  is  conceivable  that 
bees  can  communicate  by  both  methods.  This  would 
become  a  new  hypothesis,  to  be  tested  in  turn  as  to  its 
correctness. 

Simple  hypotheses  concerning  single  things  or  small 
groups  of  phenomena  are  much  more  easily  tested  than 
those  which  involve  a  large  number  of  facts.  The  law 
for  the  diffusion  of  light  when  it  was  in  the  hypothetical 
state  could  easily  be  tested,  but  such  vast  systems  of  re- 
lations as  are  involved  in  the  nebular  hypothesis,  or  the  doc- 
trine of  evolution,  permit  of  but  partial  verification  at  any 
one  time.  The  cumulative  labors  of  generations  of  schol- 
ars are  often  inadequate  to  their  complete  demonstration. 
Hypotheses  suitable  for  students  in  testing  as  to  fact  are 
naturally  of  the  simpler  sort. 

DISCUSSION:  —  Difference  between  unexplained  difficulties 
in  an  hypothesis  and  the  failure  to  stand  the  test  of  fact.  Com- 
pare the  undulatory  and  the  corpuscular,  or  emanation,  theory 
of  light  in  this  respect.1  Use  also  illustrations  from  daily 
life,  detective  stories,  etc. 

1  See  William  Stanley  Jevons,  "Principles  o£  Science,"  p.  510. 


THE    MEANING    OF    FACTS  —  THEIR    EXPLANATION     37 

(5)    The  Experimentum  Crucis 

20.  It  not  infrequently  happens  that  each  of  two  hy- 
potheses explains  so  many  facts  that  both  find  many 
advocates.  This  has  often  been  the  case  in  the  history  of 
science.  An  experiment  that  decides  between  two  rival 
hypotheses  is  called  an  experimentum  crucis  (experiment 
of  the  finger-post). 

As  Jevons  1  says,  the  long-continued  strife  between  the 
corpuscular  and  the  undulatory  theories  of  light  furnishes 
the  most  beautiful  examples  of  the  experimentum  crucis. 
Both  theories  furnish  satisfactory  explanations  of  many 
phenomena  of  light,  such  as  reflection  and  refraction.  If, 
however,  the  undulatory  theory  be  correct,  light  must 
move  more  slowly  hi  a  dense  than  in  a  rare  medium, 
whereas,  on  the  other  hand,  if  the  corpuscular  theory  were 
true,  the  reverse  would  be  the  case,  for  the  denser  medium 
would  have  an  attractive  power  which,  exerted  at  infin- 
itesimal distances,  would  accelerate  the  speed  of  the  light 
particles.  Here  was  a  chance  for  a  single  experiment  to 
disprove  one  hypothesis  while  proving  the  other.  Fou- 
cault  compared  directly  the  speeds  of  two  beams  of  light, 
one  passing  through  air  only,  the  other  through  several 
meters  of  water  as  a  part  of  its  path,  and  found  that  light 
passes  more  slowly  through  water  than  through  air.1 

1  See  "Principles  of  Science,"  pp.  520,  521. 

'Paul  Drude,  "Lehrbuch  der  Optik,"  pp.  111-113. 

95361 


38      SCIENTIFIC    BASIS    FOR    HIGH-SCHOOL    METHODS 

A  modern  instance  is  seen  in  the  series  of  Havana  ex- 
periments to  decide  which  is  correct,  the  theory  that  yel- 
low fever  is  caused  by  infection  or  contagion,  or  the  more 
modern  rival  hypothesis  that  it  is  due  to  inoculation 
by  the  mosquito.  These  experiments  have  two  aspects : 
first,  to  prove  that  the  disease  can  be  transmitted  by  inocu- 
lation; and  second,  that  it  cannot  be  communicated  by 
contagion.  Though  it  is  possible  and  perfectly  justifiable 
to  regard  these  experiments  as  isolated  and  each,  therefore, 
like  any  test  to  prove  or  disprove  a  theory,  yet  in  reality 
they  constitute  a  unit,  being  conceived  by  the  same  men 
and  carried  out  at  the  same  time.  For  this  reason  it  is 
perhaps  fair  to  consider  them  as  forming  in  their  totality 
an  experimentum  crucis.  To  control  conditions  for  the 
first  part  of  the  experiment,  mosquito-proof  tents  were 
constructed  in  a  dry  and  isolated  location.  Volunteers, 
including  members  of  the  medical  staff,  then  lived  in  these 
tents  and  submitted  themselves  to  the  bites  of  mosquitoes 
known  to  have  bitten  yellow  fever  patients,  and  hence  to 
be  in  a  condition  to  transmit  the  disease,  should  it  turn 
out  that  they  were  able  to  do  so.  The  experiments  were 
inconclusive,  as  earlier  ones  had  been,  when  the  period  of 
incubation  of  the  assumed  disease  germs  was  less  than 
ten  days.  One  of  the  physicians  had  been  bitten  on  the 
hand  by  a  mosquito  that  had  had  an  incubating  period 
of  six  days,  but  no  result  followed.  A  little  later,  however, 
Dr.  Lazear  permitted  a  mosquito  to  bite  him  that  had  had 


THE    MEANING    OF    FACTS  — -  THEIR    EXPLANATION      39 

an  incubating  period  of  twelve  days.  The  disease  was  then 
contracted,  and  Dr.  Lazear  lost  his  life.  Acting  on  the 
knowledge  thus  expensively  obtained,  many  others  were 
bitten  by  mosquitoes  that  had  been  infected  twelve  days 
or  more,  with  the  result  that  nearly  all  the  non-immune 
experimenters  contracted  the  disease.  Two  facts  were 
thus  established:  first,  that  yellow  fever  can  be  trans- 
mitted by  inoculation;  and  second,  that  a  period  of  incu- 
bation of  about  two  weeks  must  elapse  before  the  insect 
is  capable  of  communicating  it  to  a  human  being. 

It  now  remained  to  test  the  old  hypothesis  that  yellow 
fever  can  be  communicated  by  contagion,  or  what  is  called 
infection.  A  mosquito-proof  cabin  was  constructed, 
and  three  Americans  submitted  themselves  to  the  experi- 
ments. This  time  instead  of  utilizing  the  mosquito,  he 
was  rigorously  excluded,  and  the  contaminated  clothing 
and  bedding  of  yellow  fever  patients  were  brought  into  the 
cabin  and  handled  by  the  young  men.  They  packed  and 
unpacked  it  daily,  slept  in  the  cabin  at  night,  and  even 
wore  the  unwashed  linen  of  persons  who  had  recently 
died  of  the  disease.  This  was  kept  up  for  three  weeks, 
yet  not  one  of  the  experimenters  suffered  from  the  sup- 
posedly deadly  contagion.  In  this  manner,  disagreeable 
yet  heroic,  the  old  fear  of  contagion  was  dissipated,  and 
the  world  at  last  learned  the  truth  as  to  how  this  dread 
disease  is  spread  from  person  to  person.  The  American 
health  authorities  at  Havana  at  once  made  war  on  the 


40      SCIENTIFIC    BASIS    FOR    HIGH-SCHOOL    METHODS 

mosquito,  to  such  good  effect  that  for  the  next  two  years 
not  a  single  case  of  yellow  fever  appeared  in  this  old  city, 
which  for  four  hundred  years  had  rarely  been  free 
from  it. 

As  was  previously  intimated,  the  mosquito  has  for  a 
period  of  two  thousand  years  been  suspected  to  be  a  bearer 
of  disease,  yet  not  until  our  own  day  has  this  suspicion 
been  changed  to  certainty.  Men  are  now  able  to  combat 
intelligently  the  malarial  and  other  fevers  that  are  trans- 
mitted by  the  mosquito,  as  at  Panama,  in  tropical  Africa, 
on  the  Roman  Campagna,  in  subtropical  regions,  and 
throughout  the  temperate  regions  of  the  earth.  One  rea- 
son why  this  discovery  was  so  long  delayed  is  because  there 
are  one  hundred  and  twenty  different  kinds  of  mosquito, 
very  few  of  which  can  act  as  a  host  for  the  incubation 
of  disease  germs.  It  is  the  Culex  stegomyia  that  trans- 
mits yellow  fever,  and  the  anopheles  malaria.  Another 
sufficient  cause  of  the  delay  is  the  fact  that  bacteriological 
knowledge  is  of  very  recent  origin. 

The  future  of  every  science,  like  its  past,  bristles  with 
problems  in  which  rival  hypotheses  are  possible.  In  many 
cases  it  will  happen,  as  it  has  happened,  that  a  single 
experiment  or  series  of  experiments  will  decide  which 
hypothesis  is  correct. 

DISCUSSION  :  —  Force  of  the  objection  that  the  free  use  of 
the  hypothesis  incites  to  guessing  and  loose  thinking. 


THE    MEANING    OF    FACTS  —  THEIR    EXPLANATION     41 

(6)    Analogy  as  a  Guide  to  Discovery 

21.  Many  a  discovery  is  made  by  following  up  hints 
furnished  by  analogy.  This  was  true  in  astronomy  when 
Galileo  discovered  that  Jupiter  has  four  small  satellites 
revolving  around  it,  thus  forming  a  small  planetary  world. 
This  fact  enabled  men  by  analogy  the  more  easily  to  accept 
the  Copernican  theory  of  the  larger  solar  system.  The 
undulatory  movement  of  water  in  waves  hints  at  undula- 
tions of  air  as  the  cause  of  sound,  while  sound-waves  in 
turn  suggest  light-waves.  Biological  analogy  has  been  es- 
pecially fruitful  in  suggesting  theories  of  state  and  society.1 
Text-book  writers  hi  physics  still  use  Clerk-Maxwell's 
analogy  between  the  behavior  of  water  and  that  of  elec- 
tricity. For  example,  potential  in  the  latter  corresponds 
to  the  head  of  water  as  it  flows  from  a  higher  to  a  lower 
level;  a  current  of  electricity  corresponds  to  the  flow 
through  a  pipe  at  the  lower  level;  resistance  in  the  elec- 
tricity corresponds  to  friction  which  the  pipe  causes  to 
a  stream  of  water  flowing  through  it,  etc.  Descartes  showed 
that  every  equation  may  be  represented  by  some  curve 
or  figure  in  space,  and  that  every  bend,  point,  cusp,  or 
other  peculiarity  in  the  curve  indicates  some  peculiarity 
in  the  values  of  the  algebraic  symbols.  "It  is  impossible 

1  Compare  S.  N.  Patten,  "The  Failure  of  Biologic  Sociology,"  Pub- 
lications of  the  American  Academy  of  Political  and  Social  Science, 
No.  121. 


42      SCIENTIFIC    BASIS    FOR    HIGH-SCHOOL    METHODS 

to  describe  in  any  adequate  manner  the  importance 
of  this  discovery.  The  advantage  was  twofold:  algebra 
aided  geometry,  and  geometry  gave  reciprocal  aid  to 
algebra."  * 

DISCUSSION  :  —  Limits  to  the  validity  of  argument  by  an- 
alogy: Is  the  state  an  organism?2  Is  electricity  a  fluid? 
Does  history  'repeat'  itself?  Are  the  experiences  of  one 
people  'like'  those  of  another?  Should  American  secondary 
education  be  patterned  after  that  of  Germany  ?  Do  the  motives 
that  are  found  active  in  one  pupil  indicate  with  certainty  that 
the  same  motives  will  be  equally  powerful  with  another  ? 

1  William  Stanley  Jevons,  "Principles  of  Science,"  p.  290.    See  also 
modern  algebras  for  method  of  graphs. 

2  See  Lester  F.  Ward,   "The  Development  of  Social  Structures," 
Congress  of  Arts  and  Science,  Vol.  V,  Houghton,  Mifflin  &  Co.,  Bos- 
ton.    See  also  Mackenzie,  "Introduction  to  Social  Philosophy,"  Ch.  Ill; 
Patten,  "The  Failure  of  Biologic  Sociology,"  American  Academy  of 
Political  and  Social  Science,  Vol.  IV;  Spencer,  "Principles  of  Sociology," 
Part  II,  Ch.  X;  Wallace,  Mind,  Vol.  VIII,  "Ethics  and  Sociology." 


CHAPTER  m 
FORMS   OF  SOLUTION  FOR  THE  PROBLEM 

22.  Since  problems  of  thought  may  arise  in  any  depart- 
ment of  human  interest,  there  is  naturally  a  diversity  pos- 
sible in  the  forms  of  their  solution.    Wherever  facts  call 
for  explanation,  there  the  problem  arises,  but  the  form  of 
explanation  most  effective  depends  upon  the  nature  of 
the  problem.    Of  the  various  forms  which  solutions  may 
take,  three  are  of  especial  importance  in  education.    They 
are:  (i)  the  determination  of  the  causal  connections  of 
phenomena,  especially  of  events;   (2)  the  classification  of 
objects,  whether  as  a  process  or  a  result  already  attained; 
and  (3)  generalization  proper,  as  in  the  derivation  of  rule, 
principle,  or  law.    The  significance  and  necessity  of  these 
forms  will  become  apparent  in  subsequent  sections. 

i.   The  Determination  of  Causes:   Method  of  Agreement 
or  Difference 

23.  It  often  happens  that  explanation  is  ample  when  a 
thing  or  an  event  is  brought  under  a  general  law  already 
understood.    This  would  be  the  case  when  the  rusting  of 
iron  is  shown  to  be  a  special  example  of  combustion;  or 
when  the  falling  of  dew  is  explained  by  the  laws  of  humidity, 

43 


44      SCIENTIFIC    BASIS    FOR    HIGH-SCHOOL    METHODS 

conductivity,  and  radiation.  In  like  manner,  we  explain 
the  action  of  the  common  pump,  the  force-pump,  the  hy- 
draulic ram,  the  turbine,  the  steam  or  gas  engine,  etc. 
This  form  of  solution  holds  not  only  in  the  organic  world, 
but  it  is  of  special  importance  in  history,  which  resists 
more  or  less  stubbornly  all  attempts  to  establish  general 
laws,  such  as  those  proposed  by  Buckle  in  his  "History 
of  Civilization."  But  we  may  always  ask  the  cause  of  an 
event  or  a  series  of  events  in  human  affairs,  or  we  may 
trace  natural  events  back  to  known  causes.  Thus  Turner  * 
shows  how  the  needs  and  demands  of  our  frontier  shaped 
our  national  legislation  respecting  the  tariff,  internal  im- 
provements, and  the  disposition  of  the  public  domain,  and 
how  it  fixed  the  character  of  our  democracy.  Patten2 
shows  how  such  factors  as  "Complementary  Goods," 
"The  Imputation  of  Utility,"  "The  Mechanism  of  the 
Standard  of  Life,"  and  "The  Relative  Size  of  the  Comple- 
mentary Groups  of  Pleasure  and  Pain  "  help  to  contribute 
to  our  moral  progress.  John  Fiske  3  points  out  that  the 
chief  reason  why  George  the  Third  so  strenuously  insisted 
upon  taxation  without  representation  in  the  American 
colonies  was  that  he  was  trying  to  perpetuate  the  same 

1  "The  Significance  of  the  Frontier  in  American  History,"  Fifth  Year- 
Book,  National  Herbart  Society. 

2  S.  N.  Patten,  "Economic  Causes  of  Moral  Progress,"  Publications 
of  American  Academy  of  Political  and  Social  Science,  No.  64. 

'"War  of  Independence,"   Riverside   Library  for  Young  People, 
pp.  58-64,  69-71. 


FORMS    OF    SOLUTION    FOR    THE    PROBLEM  45 

policy  at  home,  in  order  that  he  might  control  legislation 
in  England  through  control  of  'rotten  boroughs'  and 
the  exclusion  from  Parliament  of  representatives  from 
the  rising  industrial  cities,  like  Birmingham  and  Man- 
chester. 

The  whole  of  history,  both  in  and  out  of  school,  falls 
naturally  and  hence  easily  into  the  problem  form,  in  which 
causes  are  sought  as  adequate  explanation.  For  example, 
why  should  the  reflex  influences  of  the  frontier  upon  the 
original  colonies  be  greater  than  the  opposing  European 
influences  ?  Why  did  French  dominion  in  America  spread 
so  rapidly  and  the  English  so  slowly?  What  enabled 
trappers  of  both  nations  to  penetrate  the  hostile  interior 
with  impunity?  What  were  the  causes  and  effects  of 
primitive  cooking,  manufacture  of  clothing,  heating  and 
lighting,  of  implements  of  agriculture,  hunting,  and  war- 
fare, of  means  of  transportation  ? 

24.  The  problems  of  the  social  and  political  world  call 
for  solutions  in  the  form  of  cause  or  effect.  To  illustrate : 
How  can  we  avoid  the  economic  waste  in  cities  that  arises 
from  the  primitive  device  of  having  an  independent  cook- 
ing outfit  for  each  family?  How  prevent  corruption  in 
corporations  and  public  administrative  systems?  How 
effect  reformation  through  the  punishment  of  offenders? 
How  make  it  possible  for  an  ex-convict  to  live  an  honest 
and  self-respecting  life?  What  means  should  manufac- 
turing establishments  use  to  secure  the  interested  coopera- 


46      SCIENTIFIC    BASIS    FOR    HIGH-SCHOOL    METHODS 

tion  of  their  employees  ?  Should  men  and  women  teachers 
have  the  same  salary  when  they  fill  equivalent  positions? 
To  solve  these  problems  is  to  investigate  social  and 
political  causes  and  effects,  and  to  draw  conclusions 
accordingly. 

25.  A  matter  of  great  importance  in  all  scientific  method 
is  the  presentation  of  simple  rules  of  evidence  to  be  used  in 
the  discovery  of  causes  or  effects.  A  farmer  with  a  primi- 
tive mind  may  say  that  unless  potatoes  be  planted  during 
a  given  phase  of  the  moon,  they  will  not  thrive.  When 
asked  for  his  reasons,  he  will  perhaps  cite  instances  which 
belong  to  the  category  of  coincidence  rather  than  to  that 
of  cause.  He  knows,  or  at  least  applies,  no  accepted  rules 
of  evidence,  and  is  consequently  an  easy  victim  of  super- 
stition. On  the  other  hand,  it  is  only  by  the  application 
of  well-known  criteria  of  cause  and  effect  that  men  are 
able  to  detect,  say  the  cause  of  disease.  Thus,  for  example, 
the  English  soldiers  at  Malta,  an  island  in  the  Mediterra- 
nean, had  long  been  sadly  afflicted  with  a  severe  type  of 
malarial  fever.  A  commission  of  physicians  was  sent  to 
discover  the  cause.  In  casting  about  for  a  clew  to  an  expla- 
nation of  the  disease,  the  doctors  learned  that  the  only  milk 
used  by  the  soldiers  came  from  goats.  Acting  upon  this 
hint,  it  was  found  that  a  mosquito  transmitted  the  disease 
germ  of  the  fever  to  the  goats  of  the  island,  which  served 
as  hosts  for  its  incubation.  When  the  recommendation 
of  the  commission  that  canned  cow's  milk  be  substituted 


FORMS    OF    SOLUTION    FOR    THE    PROBLEM  47 

for  the  goat's  milk  heretofore  used  was  followed,  the  dis- 
ease entirely  disappeared.  A  primitive  man  would  per- 
haps have  tried  by  incantations  to  exorcise  the  demons 
that  were  afflicting  the  men,  or  he  would  have  ascribed 
the  disease  to  the  inscrutable  will  of  some  overruling 
power,  whose  wrath  it  were  impossible  to  appease. 

These  scientific  rules  of  evidence,  rigidly  applied,  have 
been  an  important  cause  of  the  modern  advance  in  knowl- 
edge, not  only  in  pure  science,  human  and  natural,  but  also 
in  their  practical  application.  It  has  become  almost  an 
instinct  with  investigators  in  every  field  of  research  to 
accept  no  evidence  that  does  not  stand  the  test  of  these 
simple  principles. 

26.  In  a  final  analysis  all  the  rules  of  evidence,  and  J.  S. 
Mill  gives  an  exposition  of  five,  rest  upon  agreement  or  dif- 
ference among  the  phenomena.  Thus,  if  two  things  agree 
in  only  one  circumstance,  being  different  in  every  other 
respect,  it  is  evident  that  the  characteristic  in  which  they 
agree  must  be  the  cause  or  effect  of  the  phenomenon  in 
question.  Or,  again,  if  two  phenomena  differ  by  only  one 
circumstance,  agreeing  in  all  others,  it  is  equally  evident 
that  the  element  of  difference  must  be  the  cause  or  effect 
of  the  phenomenon  in  question.  The  three  remaining 
modes  of  proof  are  only  combinations  of  the  two  just 
mentioned.  The  five  methods  elaborated  by  Mill l  will 
now  be  taken  up  in  detail  for  definition  and  illustration. 

1  "Logic,"  Book  III,  Ch.  VIII. 


48      SCIENTIFIC    BASIS    FOR    HIGH- SCHOOL    METHODS 

(i)  The  Method  of  Agreement 

27.  When  two  or  more  instances  of  a  phenomenon 
have  only  one  circumstance  in  common,  differing  in  all 
other  particulars,  the  circumstance  in  which  they  agree  is 
the  cause  of  the  phenomenon  in  question. 

The  Havana  experiments  as  to  the  cause  of  transmission 
in  yellow  fever  described  above  illustrate  the  method  of 
agreement.  The  two  groups  concerned  were  the  victims 
of  the  disease  in  the  city  at  large,  on  the  one  hand,  and  the 
future  possible  patients  under  the  control  of  the  experi- 
menters on  the  other.  It  will  be  remembered  that  there 
were  two  hypotheses  concerning  the  way  in  which  the 
disease  is  transmitted,  namely,  by  contagion  or  infection 
through  the  air,  and  by  inoculation  by  mosquitoes.  (See 
p.  38.)  If  now  the  two  groups  can  be  so  situated  that 
only  one  possible  cause  of  transmission  is  common  to 
both,  the  groups  differing  in  all  other  essential  particu- 
lars, it  is  certain  that  the  true  cause  will  be  revealed,  should 
the  new  group  develop  the  fever  under  these  conditions. 
Since  the  belief  of  the  experimenters  was  that  the  disease 
is  occasioned  by  inoculation,  they  first  isolated  them- 
selves from  all  possible  contagion  or  infection  by  select- 
ing a  high  and  dry  location  sufficiently  remote  from  the 
city,  and  rigorously  quarantining  themselves.  They  next 
made  mosquito-proof  tents  in  which  to  live,  that  they  might 
suffer  no  general  danger  from  this  source  such  as  the  town 


FORMS    OF    SOLUTION    FOR    THE    PROBLEM  49 

patients  were  exposed  to.  They  then  suffered  themselves 
to  be  bitten  by  mosquitoes  taken  from  the  sick  rooms  of 
yellow  fever  patients  in  the  city,  and  which  were  known  to 
be  contaminated.  It  will  be  seen  that  this  circumstance 
of  being  bitten  by  contaminated  mosquitoes  was  the  only 
common  probable  cause  of  the  disease,  the  two  groups  being 
different  as  respects  exposure  to  other  causes,  and  when  a 
large  per  cent,  of  the  experimenters  so  bitten  contracted  the 
fever,  it  was  certain  that  inoculation  is  one  cause  of  trans- 
mission, and  perhaps  the  only  cause.  To  make  the  latter 
point  more  certain,  the  other  series  of  experiments  was 
arranged  to  prove  that  it  is  not  transmitted  by  contagion. 
As  before,  all  possible  causes  of  the  disease  except  the  one 
hypothetical  cause  of  contagion  were  excluded,  so  that  the 
two  groups  again  differed  in  all  essential  conditions  except 
this  one.  The  three  young  Americans  who  submitted 
themselves  to  this  experiment  were  isolated  in  a  mosquito- 
proof  cabin  so  constructed  that  sunlight  and  fresh  air  were 
largely  excluded.  They  then  handled  freely  the  contami- 
nated clothing  and  other  effects  of  the  town  patients, 
even  sleeping  in  the  soiled  linen  of  those  who  had  died. 
When,  at  the  end  of  twenty-one  days,  all  three  remained  in 
perfect  health,  it  was  held  that  the  disease  is  not  trans- 
mitted by  contagion,  and  that  the  former  expensive  custom 
of  fumigating  or  burning  all  effects  coming  from  an  in- 
fected district  is  quite  unnecessary. 

DISCUSSION: —  i.  Cause  of  typhoid  fever  in  half  a  dozen 


50      SCIENTIFIC    BASIS    FOR    HIGH-SCHOOL    METHODS 

given  cases  in  which  it  is  found  that  they  all  agree  in  one 
circumstance  that  might  be  a  cause.  2.  The  use  of  this  method 
in  showing  the  conversion  of  solids  into  liquids  and  of  liquids 
into  gases  by  means  of  heat;  in  showing  the  injurious  effect 
of  northeast  winds  (think  of  temperature,  violence,  moisture, 
electricity,  ozone  as  differing,  but  in  all  cases  bear  in  mind  the 
close  contact  of  the  air  with  the  ground  for  long  distances).1 

(2)  The  Method  of  Difference 

28.  Where  two  instances  differ  in  only  one  circumstance, 
agreeing  in  all  others,  the  circumstance  in  which  they  differ 
is  the  cause  (or  effect)  sought. 

The  Malta  investigation  (see  p.  46)  illustrates  the  use 
of  the  method  of  difference.  The  two  groups  in  this  case 
are  the  English  soldiers  at  Malta  who  suffered  from  a 
particular  malarial  fever,  and  English  soldiers  in  India, 
Egypt,  and  other  semi-tropical  regions  who  do  not.  Is 
there  any  one  circumstance  that  might  be  a  cause  wherein 
the  Malta  group  differs  from  the  others  ?  Evidently  they 
agree  in  most  particulars,  coming  from  the  same  country, 
living  in  the  same  kind  of  climate,  under  the  same  disci- 
pline, and  eating  the  same  rations.  If  such  a  differing  cir- 
cumstance having  any  relation  to  the  possible  cause  can 
be  found,  it  should  be  investigated.  Searching  for  a  clew 
of  this  kind,  the  physicians  learned  that  the  Malta  soldiers 
used  goat's  milk,  whereas  the  others  (presumably)  did 

1  See  Alexander  Bain,  "  Logic-Induction,"  p.  53. 


FORMS  OF  SOLUTION  FOR  THE  PROBLEM      51 

not.  Investigation  of  this  milk  revealed  malarial  germs, 
which  were  then  traced  back  to  the  mosquito.  The  cor- 
rectness of  this  conclusion  from  the  element  of  difference 
is  confirmed  by  the  fact  that  when  canned  cow's  milk  was 
substituted,  the  disease  disappeared. 

DISCUSSION: — i.  Amount  of  rain  that  falls  at  the  surface 
of  the  earth  and  at  a  considerable  elevation  (the  element  of 
difference  being  the  effect  of  wind).  2.  Probable  cause  of  dif- 
ference in  prosperity  of  farmers  living  under  the  same  conditions. 
3.  Why  is  one  day  at  school  more  trying  than  another  to  the 
teacher  ?  4.  Show  that  heat  is  the  cause  of  the  melting  of  ice, 
wax,  or  lead  by  making  the  raising  of  temperature  the  only 
change.  5.  How  prove  the  operative  force  of  drugs  which 
produce  immediate  effects ;  remote  ones.  6.  Need  of  knowing 
beforehand  the  general  adequacy  of  the  cause  assigned. 

(3)  The  Joint  Method  of  Agreement  and  Difference 

29.  "A  number  of  instances  having  been  examined, 
whatever  is  invariably  present  when  the  phenomenon 
under  investigation  is  present,  and  invariably  absent  when 
the  latter  is  absent,  is  causally  connected  with  that  phe- 
nomenon." * 

This,  it  may  be  seen,  is  a  combination  of  the  two  methods 
described  above,  for  in  the  first  part  we  have  agreement, 
and  in  the  second  difference.  Suppose  the  problem  to 
be  to  find  the  cause  of  a  case  of  indigestion.  We  may 
examine  a  series  of  instances  in  which  cereals  with  and 

1  J.  E.  Creighton,  "Introductory  Logic,"  p.  209. 


52      SCIENTIFIC    BASIS    FOR    HIGH-SCHOOL    METHODS 

without  cellulose  are  eaten  at  different  periods;  when 
coffee  or  any  other  beverage  is  used  alternately  and  dis- 
continued; or  when  the  diet  is  chiefly  vegetable,  then  chiefly 
meat,  etc.  If,  for  example,  the  symptoms  of  indigestion 
invariably  accompany  the  free  use  of  coffee  and  as  inva- 
riably subside  upon  its  discontinuance,  we  may  be  sure 
that  coffee  is  causally  connected  with  the  indisposition. 
In  similar  manner,  one  may  investigate  causes  of  disorder 
at  school,  the  interest  and  success  or  failure  of  students  in 
their  work,  etc. 

(4)  The  Method  of  Concomitant  Variations 

30.  Mill  says,  "Whenever  in  two  instances  any  particu- 
lar phenomenon  varies  in  any  manner,  whenever  another 
phenomenon  varies  in  a  particular  manner,  the  first  vary- 
ing phenomenon  is  either  a  cause  or  an  effect  of  the  second, 
or  is  connected  with  it  through  some  fact  of  causation." 
Suppose,  for  illustration,  heat  is  the  first  varying  phenome- 
non and  friction  the  second.  If  now  the  friction  increases 
and  it  is  found  that  the  temperature  of  the  body  rubbed 
increases  correspondingly,  we  may  be  sure  that  friction 
is  a  cause  of  heat.  Concomitant  variations  are  therefore 
evidences  of  cause  and  effect.  Any  increase  or  decrease 
in  the  cause  is  marked  by  a  corresponding  variation  in  the 
effect.  Whenever,  therefore,  the  variations  run  parallel 
to  the  changes  in  the  cause,  thus  making  the  changing 
effects  keep  pace  with  the  changing  causes,  we  may  be 


FORMS  OF  SOLUTION  FOR  THE  PROBLEM      53 

sure  that  we  have  discovered  the  cause  or  effect  of  the 
phenomenon  in  question.  Thus  in  testing  the  toxic  effect 
of  vanillin  upon  plant  growth,  the  experimenters  of  the 
Bureau  of  Agriculture  caused  a  set  of  seeds  to  germinate 
under  conditions  that  were  exactly  alike,  except  that  the 
amount  of  vanillin  applied  varied,  say  as  i,  20,  40, 100,  500. 
Photographs  showing  the  growth  of  tops  and  roots  at  the 
end  of  a  given  period  revealed  the  fact  that  for  each  increase 
of  vanillin  there  was  a  corresponding  decrease  in  the 
amount  of  growth,  hence  a  concomitant  variation  between 
the  toxic  cause,  vanillin,  and  the  growth  effect.  The 
inevitable  conclusion  is  that  in  this  case  vanillin  is  a  poison 
to  vegetable  growth. 

The  experiment  of  carrying  a  barometer  to  the  top  of 
a  mountain  is  a  proof  by  variation  of  the  connection  be- 
tween the  pressure  of  the  air  and  the  rise  of  the  mercury. 

DISCUSSION:  —  Test  by  the  method  of  concomitant  varia- 
tions the  influence  of  increasing  or  decreasing  heat  upon  evap- 
oration, plant  growth,  expansion  of  metals;  of  increasing 
income  upon  the  number  and  quality  of  schools  (see  statistics), 
marriage,  birth-rate,  etc. 

(5)    The  Method  of  Residues 

31.  Mill  defines  this  method  as  follows:  "Subduct  from 
any  phenomenon  such  part  as  is  known  by  previous  in- 
ductions to  be  the  effect  of  certain  antecedents,  and  the 
residue  of  the  phenomenon  is  the  effect  of  the  remaining 
antecedents." 


54      SCIENTIFIC    BASIS    FOR    HIGH-SCHOOL    METHODS 

When  many  general  causes  of  phenomena  become  well 
known,  the  solution  of  new  problems  is  greatly  simplified 
by  subducting  the  influence  of  causes  that  are  known  to 
be  active  in  the  given  case.  The  most  brilliant  example 
of  the  application  of  this  method  in  astronomy  was  the 
clew  to  the  discovery  of  Neptune  furnished  by  certain 
anomalies  then  unaccounted  for  in  the  motion  of  Uranus. 
Adams  and  Le  Verrier  by  mathematical  calculation  located 
in  space  the  probable  cause  of  the  irregularity  by  deducting 
the  effects  of  known  causes,  and  invited  the  astronomers  to 
direct  their  telescopes  to  this  spot  in  the  heavens.  They 
did  so,  and  the  new  planet  Neptune  became  a  recognized 
member  of  the  solar  family.  The  observation  of  Arago, 
that  a  magnetic  needle,  set  to  vibrating,  is  sooner  brought 
to  rest  when  suspended  over  a  copper  plate,  was  the  first 
clew  to  the  discovery  of  magneto-electricity.1  Similarly, 
the  observation  of  Cavendish  that  when  the  known  con- 
stituents of  the  air  were  deducted,  there  was  left  a  small 
residuum  unaccounted  for,  which  in  1895  was  proved  to 
be  a  new  element  by  Lord  Rayleigh  and  William  Ramsay. 
They  named  it  argon  (lazy),  from  its  inert  character. 

The  method  of  residues  is  available  in  accounting  for 
unforeseen  effects  of  legislation  or  of  new  inventions.  In 
this  way  we  may  account  for  the  influence  of  the  sewing- 
machine  and  the  bicycle  upon  woman's  clothing,  of  the 
electric  illumination  of  streets  at  night  upon  crime,  of  the 

*See  Bain,  "Logic-Induction,"  p.  66. 


FORMS    OF    SOLUTION    FOR    THE    PROBLEM  55 

invention  of  the  cotton-gin  upon  slavery  north  and  south, 
etc.  As  Bain  remarks,  "  The  only  proof  of  an  exhaustive 
analysis,  whether  in  material  actions  or  in  mental  pro- 
cesses, is  there  being  nothing  left."  This  being  the  case, 
we  may  investigate  such  disputed  points  as  the  existence 
or  non-existence  of  innate  ideas,  the  moral  sense,  the  free- 
dom of  the  will,  etc.,  by  deducting  the  known  constituent 
causes  of  mental  life.  If  these  completely  account  for  the 
phenomenon  in  question,  then,  since  there  is  nothing  left, 
the  problem  is  solved.  Or,  if  there  is  something  still 
unaccounted  for,  a  different  solution  is  indicated. 

DISCUSSION  :  —  Apply  the  method  of  residues  to  explain 
why  the  south  shore  of  Lake  Erie  has  become  the  richest 
stretch  of  coast  of  like  length  in  the  world. 

2.  Classification 

32.  In  a  last  analysis  nearly  all  thinking  involves 
classification,  for  when  we  affirm  one  thing  or  another, 
we  put  them  by  implication  in  the  same  class.  Every 
common  noun  to  be  found  hi  the  dictionary  is  the  name 
of  a  class,  and  in  the  class  we  find  the  meaning  of  con- 
cept, or  general  notion.  Usage,  however,  limits  the  term 
classification  to  certain  cases.  Thus  we  speak  of  the  con- 
cept triangle,  but  of  the  class  mammalia;  yet  the  reverse 
of  this  custom  is  logically  justifiable.  Bain  uses  the 
term  sciences  of  classification  for  botany,  zoology,  and 
mineralogy.  To  these  we  may  add  a  considerable  part  of 


56      SCIENTIFIC    BASIS    FOR    HIGH-SCHOOL    METHODS 

grammar.  In  the  words  of  Huxley,  "  By  the  classification 
of  any  series  of  objects  is  meant  the  actual  or  ideal  arrange- 
ment together  of  those  which  are  like  and  the  separation 
of  those  which  are  unlike;  the  purpose  of  this  arrange- 
ment being  to  facilitate  the  operations  of  the  mind  in 
clearly  conceiving  and  retaining  in  the  memory  the  char- 
acters of  the  objects  in  question."  By  means  of  classifica- 
tion we  condense  and  systematize  our  knowledge,  thus 
making  it  manageable,  and  enabling  us  to  forecast  resem- 
blances in  objects  not  yet  examined,  and  even  to  discover 
laws  of  nature. 

33.  The  possible  modes  of  classification  are  practically 
unlimited  in  extent,  since  classes  may  be  formed  upon  any 
basis  that  chances  to  be  convenient.    For  illustration, 
crystals  may  be  classified  according  to  their  composition 
or  their  form;  plants  may  be  and  have  been  classified  on 
the  basis  of  their  fruits,  their  leaves,  or  the  corolla  or  the 
calyx  of  their  flowers;  men  are  classified  as  to  race,  color, 
occupation,  economic  station,  politics,  religion,  disposition, 
nationality,  etc.;   animals  may  be  classified  according  to 
form,  function,  manner  of  getting  food,  manner  of  repro- 
duction, color,  feet,  legs,  horns,  skins,  etc. 

DISCUSSION:  —  Practical    exercises    in    the    classification 
of  leaves;  of  pictures.1 

34.  Scientific  classification  rejects  accidental  or  unim- 

1  See  the  author's  "  Laboratory  Exercises  in  Art  Appreciation,"  C.  W. 
Bardeen,  Syracuse,  N.Y. 


FORMS    OF    SOLUTION    FOR    THE    PROBLEM  57 

portant  characteristics  as  a  basis,  and  seeks  out  those  that 
are  most  important,  and  in  the  case  of  living  beings  those 
which  best  represent  the  conditions  for  survival  for  the 
object.  The  classification  ruminant  is  a  more  scientific 
one  than  that  of  pachyderm,  since  the  manner  of  prepar- 
ing the  food  for  digestion  is  a  more  important  requisite 
for  the  survival  of  the  animal  than  the  thickness  of  the 
skin.  What  Bain  calls  the  Golden  Rule  of  classification 
is  stated  as  follows :  Of  the  various  groupings  of  resem- 
bling things,  preference  is  given  to  such  as  have  in  common 
the  most  numerous  and  the  most  important  attributes.  The 
whale  is  to  be  classed  with  mammals  rather  than  with 
fish,  because  the  manner  of  bringing  forth  the  young  is 
more  important  than  the  fact  that  it  lives  in  the  water 
like  a  fish.  Yet  we  may  speak  of  the  whale  fishery,  since 
the  purpose  of  classification  is  now  practical  convenience, 
rather  than  scientific  accuracy. 

35.  A  pedagogical  device  of  much  importance  is  the 
use  of  the  type  as  the  basis  of  classification.  So  intricate 
is  the  classification  of  living  objects  that  biologists  often 
select  for  their  students  a  representative  or  typical  plant 
or  animal,  and  make  a  detailed  study  of  its  characteristics. 
They  then  refer  all  similar  objects  to  the  type,  calling 
attention  at  the  same  time  to  important  variations.  This 
method,  though  subject  to  grave  logical  objections  as  a 
scientific  method  for  classification,  has  great  advantages 
for  teaching,  since  it  enables  the  student  to  get  a  working 


58      SCIENTIFIC    BASIS    FOR    HIGH- SCHOOL    METHODS 

idea  of  large  classes  of  plants  or  animals  by  careful  study 
of  a  few  types. 

DISCUSSION  :  —  Comparative  value  of  text-books  of  this 
kind,  especially  for  dissection  purposes.  See  Colton's  "Prac- 
tical Zoology,"  in  which  such  types  as  the  grasshopper,  the 
cricket,  the  beetle,  the  crayfish,  the  earthworm,  the  fish,  the 
turtle,  the  rabbit,  etc.,  are  studied  in  detail.  See  also  Boyer's 
"Elementary  Biology,"  in  which  on  the  plant  side  such  types 
as  the  following  are  taken  up  in  detail:  green  slime  and  the 
yeast-plant,  brook  silk,  green  felt,  stonewort,  liverwort,  com- 
mon fern,  Scotch  pine,  trillium,  seeds  and  seedlings.  Need- 
ham's  "Elementary  Zoology"  selects  the  following  types  among 
the  vertebrates:  the  catfish,  the  frog,  the  turtle,  the  snake, 
the  English  sparrow,  the  rabbit. 

36.  It  is  not  the  purpose  of  the  present  exposition  to 
explain  the  manifold  rules  and  intricacies  of  classification, 
yet  it  may  be  well  for  the  future  teacher  to  realize  that  they 
exist,  and  may  be  studied  in  such  works  as  Mill's  "Logic," 
Bain's  "Logic-Induction,"  Jevon's  "Principles  of  Sci- 
ence," and  in  many  similar  treatises.  A  quotation  from 
Colton's  "Zoology,  Descriptive  and  Practical"  will  illus- 
trate the  perplexities  of  the  investigator  when  he  is  on  the 
borderland  that  divides  the  classes.  "It  might,  at  first 
thought,  seem  strange  that  so  simple  an  animal  as  the  lance- 
let  should  be  classed  with  a  group  having  such  complex 
structure  as  the  vertebrates.  The  lancelet  has,  in  fact, 
been  placed  with  the  mollusks,  and  later  with  the  fishes, 
but  is  now  located  at  the  foot  of  the  vertebrate  series, 


FORMS    OF    SOLUTION    FOR    THE    PROBLEM  59 

chiefly  on  account  of  the  possession  of  the  notochord  and 
the  dorsal  nervous  system.  It  is  really  hard  to  locate 
an  animal  with  colorless  blood,  and  with  neither  skull, 
brain,  heart,  auditory  organs,  paired  eyes,  nor  paired  fins. 

"The  student  who  gets  his  ideas  of  classification  almost 
entirely  from  reading  is  apt  to  think  that  the  animal  king- 
dom is  divided  into  groups  separated  by  clear  and  distinct 
dividing  lines.  But  when  he  undertakes  the  actual  exami- 
nation of  any  considerable  series  of  animals,  he  often  finds 
that  two  groups  which  he  regarded  as  distinct  actually 
merge  one  into  the  other  so  gradually  that  he  finds  it 
difficult  to  see  just  where  the  line  of  division  should  be 
drawn.  The  line  of  demarcation  must  frequently  be  so 
drawn  that  it  cuts  across  some  intermediate  forms,  part 
of  whose  characteristics  lie  on  one  side  and  part  on  the 
other.  In  some  cases  the  intermediate  forms  are  living; 
in  other  cases  the  'connecting  links'  are  represented  only 
by  fossil  forms,  as,  for  example,  the  extinct  animals  that 
connect  the  reptiles  and  the  birds. 

"The  lancelets  are  plainly  on  the  threshold  of  the  ver- 
tebrate household.  By  some  authorities  they  are  denied 
admittance,  and  must  wait  just  outside.  Others  allow 
them  barely  to  cross  the  threshold  and  humbly  take  their 
place  by  the  door,  the  lowest  of  the  great  branch  at  whose 
head  stands  man. 

"On  account  of  the  poorly  developed  brain  and  the 
absence  of  a  cranium,  the  lancelet  is  placed  by  itself  in  a 


60      SCIENTIFIC    BASIS    FOR    HIGH-SCHOOL    METHODS 

division  called  Acrania,  while  all  the  other  vertebrates  are 
designated  as  Craniata,  from  the  presence  of  a  skull  and 
the  higher  development  of  the  brain."  1 

DISCUSSION: — i.  Place  and  importance  of  classification  in 
the  various  high-school  studies.  2.  Utilization  of  the  collect- 
ing instinct  among  children. 

3.   Generalization 

(i)  Non-Mathematical  Generalizations 

37.  Thus  far  two  essential  forms  of  explanation,  or  the 
solution  of  problems,  have  been  discussed,  namely,  ex- 
planation by  the  assignment  of  adequate  cause  and  that 
form  of  condensation  known  as  classification.  Planetary 
motion  is  explained  when  the  two  causes,  gravity  and  tan- 
gential velocity,  are  pointed  out.  The  propulsion  of  a  bul- 
let following  the  pulling  of  a  trigger  is  explained  when  the 
series  of  intermediate  causes,  concussion,  heat,  ignition  of 
powder,  generation  of  gases,  is  made  clear.  What  to  a 
savage  is  a  miraculous  occurrence,  becomes  a  natural 
series  of  effects  to  the  man  by  whom  the  explanation  has 
been  understood.  In  like  manner,  even  the  most  unusual 
forms  of  plant  and  animal  life  are  rendered  intelligible 
when  through  classification  they  have  been  brought  into 
proper  relation  to  well-known  objects. 

1  Pp.  152, 153. 


FORMS    OF    SOLUTION    FOR    THE    PROBLEM  6l 

38.  The  third  form  of  explanation  most  valuable  in 
education  is  that  known  as  generalization.    As  the  term 
is  usually  understood  by  logicians,  generalization  means 
passing  by  inductive  reasoning  from  a  fact  or  a  group  of 
facts  to  a  multitude  of  unexamined  cases,  which  we  believe 
to  be  subject  to  like  conditions;   as  when,  for  example, 
from  the  examination  of  one  specimen  of  the  death's-head 
moth  we  assume  that  the  same  characteristics  will  be  found 
in  all  other  members  of  the  same  class.    Instead  of  having 
to  wait  until  we  can  take  a  trip  to  Germany  to  see  and 
recognize  the  same  peculiarities  in  other  specimens  of  this 
moth,  we  jump  immediately  to  the  conclusion  that  if  there 
are  other  examples  of  it  in  existence,  they  will  have  these 
same  unusual  marks  of  skull  and  cross-bones  on  their 
backs.    If  one  piece  of  iron  expands  when  we  apply  heat 
to  it,  we  assume  at  once  that  all  other  pieces  of  iron  (and 
perhaps  other  metals  as  well)  will  behave  in  like  manner 
under  the  same  condition.    When  one  comet  was  shown 
to  obey  the  force  of  gravity,  it  was  considered  certain  that 
all  similar  bodies  are  obedient  to  the  same  force. 

39.  A  less  formal  and  definite  act  of  generalization  is 
performed  when  we  recognize  even  in  two  facts  a  common 
nature.    Thus,  before  the  nature  of  the  rainbow  was  under- 
stood, Roger  Bacon  called  attention  to  other  objects  which 
present  a  similar  appearance,  as,  for  instance,  when  the 
sun  is  shining  on  drops  of  water  dashed  up  by  the  oar,  or 
the  spray  from  a  waterfall,  or  the  dew  on  the  grass,  or  the 


62      SCIENTIFIC    BASIS    FOR    HIGH-SCHOOL    METHODS 

ice  crystals  on  the  trees  after  a  sleet  storm,  or  even  hexag- 
onal crystals  from  Ireland  or  India  and  other  transparent 
stones.  "No  sooner  have  we  grouped  together  these 
apparently  diverse  instances,  than  we  have  begun  to 
generalize,  and  have  acquired  a  power  of  applying  to  one 
instance  what  we  can  detect  of  others.  Even  when  we  do 
not  apply  the  knowledge  gained  to  new  objects,  our  com- 
prehension of  those  already  observed  is  greatly  strengthened 
and  deepened  by  learning  to  view  them  as  particular  cases 
of  a  more  general  property."  1 

40.  The  formation  of  inductive  generalizations,  as 
above  described,  serves  a  double  purpose  to  the  investi- 
gator; for  in  the  first  case,  it  enables  him  to  discover  and 
formulate  that  which  is  common  among  the  manifold, 
that  is,  to  arrive  at  rules,  laws,  and  causal  principles;  and 
in  the  second  place,  it  enables  him  in  turn  to  utilize  these 
generalizations  for  the  explanation  of  new  facts.  For 
illustration,  when  Newton  had  once  arrived  at  the  grand 
generalization  called  the  law  of  gravitation,  the  motions 
of  all  the  heavenly  bodies  could  be  explained  by  its  aid. 
Inductive  research  enabled  men  to  discover  the  laws  of 
humidity,  conduction,  and  radiation,  while  these  laws  in 
turn  enabled  them  to  explain  the  causes  of  dew,  which 
up  to  that  time  had  baffled  all  efforts  to  understand  it. 
When  once  combustion  had  been  recognized  as  oxidation, 
a  host  of  hitherto  unexplained  phenomena,  like  those  per- 

1  William  Stanley  Jevons,  "  Principles  of  Science,"  p.  598. 


FORMS    OF    SOLUTION    FOR    THE    PROBLEM  63 

taining  to  fire  and  the  rusting  of  metals,  could  easily  be 
explained.  Indeed,  the  development  of  all  science,  both 
human  and  natural,  is  closely  associated  and  dependent 
upon  this  form  of  explanation.  Its  use  in  secondary  edu- 
cation will  be  duly  emphasized  in  the  chapters  which  fol- 
low. 

(2)  Mathematical  Generalizations 

41.  As  is  well  known,  there  is  a  class  of  general  prin- 
ciples which  for  want  of  a  better  name  may  be  called  gen- 
eralizations, and  which  differ  essentially  from  the  generali- 
zations that  arise  from  induction  in  that  they  are  open  to 
demonstration,  and  hence  have  more  than  inductive  cer- 
tainty. From  the  standpoint  of  the  teacher,  however, 
they  may  well  be  termed  generalizations,  since  they  may  be 
approached  by  experience  as  acquired  by  observation  and 
constructive  experiment.  In  fact,  they  are  most  readily 
apprehended  and  best  retained  when  approached  by  con- 
crete cases,  and  whenever  possible  by  inductive  methods. 
The  history  of  mathematics  shows  that  this  has  been  the 
order  of  initial  acquisition.  Illustrations  are  seen  in  the 
fact  that  the  Romans  used  pebbles  (calculi)  to  aid  in  the 
simple  rules  of  arithmetic;  that  the  Chinese  use  the  abacus 
for  computation  in  the  same  way  as  do  our  primary  schools ; 
that  the  Egyptians  learned  a  number  of  geometrical  truths 
by  mastering  problems  that  arose  in  connection  with  the 
survey  of  their  lands;  while  we  may  well  conceive  that 


64      SCIENTIFIC    BASIS    FOR    HIGH-SCHOOL    METHODS 

much  of  the  earlier  development  was  incited  by  concrete 
constructive  methods.  All  exact  quantitative  science  owes 
its  existence  largely  to  the  fact,  first,  that  great  minds 
have  discovered  and  developed  systems  of  mathematical 
generalizations,  and  second,  that  other  great  minds  have 
applied  them  in  the  explanation  of  hitherto  uncompre- 
hended  phenomena. 

42.  In  briefest  outline  we  have  now  passed  in  review 
the  methods  whereby  the  busy  outside  world  acquires  its 
experience,  how  it  explains  its  observations,  sets  and  solves 
its  problems,  and  the  leading  forms  which  these  solutions 
take.  We  have  seen  what  use  is  made  of  authority,  ob- 
servation, experiment,  hypothesis,  analogy,  the  problem, 
causation,  classification,  and  generalization.  It  now  be- 
comes our  task  to  examine  in  some  detail  what  use  the  high 
school  should  make  of  these  great  instruments  of  acquisi- 
tion and  comprehension  as  it  trains  the  youth  of  the  land 
to  meet  successfully  the  situations  of  the  adult  world. 


B.    SCIENTIFIC    METHOD    IN    HIGH-SCHOOL 
INSTRUCTION 


CHAPTER  IV 

THE  EDUCATIONAL  STATUS   OF  THE  HIGH- 
SCHOOL  STUDENT 

43.  In  order  to  produce  its  best  results  in  the  high- 
school,  scientific  method,  though  preserving  its  original 
spirit,  must  undergo  certain  modifications  necessitated  by 
the  educational  status  of  the  student  in  secondary  educa- 
tion.   What  this  status  is  may  be  seen  by  comparing  it 
with  that  of  the  man  of  research.    This  comparison  in- 
volves three  important  points,  namely,  (i)  location  in  the 
field  of  knowledge;    (2)  amount  of  knowledge  to  be  ac- 
quired ;  and  (3)  efficiency  in  the  use  of  what  is  acquired. 

44.  In  determining  the  whereabouts  of  the  student  in  the 
domain  of  knowledge,  we  have  first  to  consider  that  he 
stands  at  the  frontiers  of  his  own  knowledge,  not  at  those 
of  the  race.    The  answers  to  his  problems  are  known,  pre- 
sumably to  the  teacher,  at  any  rate  by  somebody;  whereas 
the  answers  to  the  problems  of  the  investigator  are  yet  to 
be  learned.     So  momentous  are  the  effects  of  this  differ- 
ence that  not  seldom  in  the  history  of  education  do  we 
find  periods  or  movements  wherein  instruction  becomes 
merely   authoritative   transmission   of   information   con- 
cerning facts  and  principles.    Indeed,  this  is  the  standard 

67 


68  SCIENTIFIC    METHOD    IN    INSTRUCTION 

method  for  the  suppression  of  individuality,  as  may  be 
seen  from  its  permanent  applications  in  the  orient  and  its 
occasional  ones  in  the  Occident.  Any  system  of  education 
that  can  successfully  exalt  memory  and  suppress  thought, 
that  can  eliminate  observation,  experiment,  problem, 
hypothesis,  and  the  verification  of  theory,  can  bring  the 
part  of  the  world  which  it  influences  to  a  static  condition, 
in  which  progress  and  individuality  are  no  longer  either 
to  be  apprehended  or  expected. 

It  is  so  much  quicker  to  tell  than  it  is  to  teach,  so  infinitely 
less  troublesome  to  state  the  facts  than  to  lead  the  student 
to  discover  them,  so  incomparably  easier  for  the  teacher 
to  state  or  point  to  cause  or  generalization  than  it  is  to  get 
the  student  to  arrive  at  either  through  his  own  thinking, 
that  indolence  often  accomplishes  that  which  is  farthest 
from  design,  namely,  the  complete  suppression  of  curiosity, 
personal  initiative,  thoughtful  mastery  of  principle  and 
efficiency  in  its  use.  With  the  investigator  it  is  different; 
nobody  can  tell  him  the  solution  of  his  problem,  for  nobody 
knows  what  it  is.  He  must  in  the  nature  of  the  case 
find  out  for  himself,  since  he  stands  at  the  frontier  of 
knowledge  itself  with  respect  to  this  one  problem.  Plainly 
it  is  an  injustice  to  the  student  to  deprive  him  of  the  satis- 
faction and  profit  of  discovery,  just  because  the  unknown 
to  him  happens  to  be  the  known  to  his  teacher.  Even  if 
the  methods  of  research  are  simplified  and  abbreviated  in 
the  case  of  the  student,  they  are  still  the  laws  for  the 


EDUCATIONAL    STATUS    OF    HIGH-SCHOOL    STUDENTS      69 

thoughtful  and  interesting  mastery  of  what  must  be 
learned.  The  joy  of  discovery  of  what  to  him  was  unknown 
is  but  a  shade  less  to  the  student  than  it  was  to  the  man  who 
first  got  the  secret  from  nature  herself.  The  same  thought- 
processes  are  involved  in  the  two  cases,  and  the  mental 
benefits  are  alike  in  kind,  even  if  not  equal  in  degree. 

These  considerations  contain  a  warning  to  the  teacher 
not  to  let  personal  ease  or  showy  but  shallow  results  conspire 
to  deprive  the  student  of  those  life-giving  thought-processes 
that  always  come  to  the  front  when  we  use,  even  if  in  modi- 
fied form,  the  methods  of  the  outside  world  as  it  solves  the 
problems  of  science  and  of  life. 

DISCUSSION: — i.  Examples  of  teaching  by  authority  re- 
corded in  the  History  of  Education.  2.  Ease  with  which 
languages,  history,  mathematics,  and  even  natural  sciences 
may  be  taught  from  the  authoritative  standpoint. 

45.  The  second  point  concerns  the  amount  of  knowledge 
to  be  acquired  by  the  student,  and  the  bearing  this  has  on 
his  method  of  acquiring  it.  The  investigator,  with  a  mind 
already  well  stored  with  knowledge,  who  has  worked  for 
months  and  even  years  to  establish  a  set  of  causal  relations 
or  to  demonstrate  a  law,  has  no  difficulty  in  remembering 
what  he  has  proved,  first,  because  of  the  vividness  of  his 
conceptions,  and  second,  because  of  their  limited  scope. 
But  the  high-school  student,  who  must  recapitulate  in 
a  brief  time,  at  least  an  epitome  of  the  acquisitions  of  the 
race,  finds  it  difficult  to  make  one  small  head  carry  all  he 


70  SCIENTIFIC    METHOD    IN    INSTRUCTION 

learns.  The  problem  may  be  stated  as  follows :  How  can 
we  utilize  the  methods  of  the  investigator,  thus  securing 
his  power,  his  initiative,  his  mental  alertness,  and  his 
general  attitude  of  mind,  and  yet  at  the  same  time  satisfy 
the  quantitative  demands  for  learning  that  are  made  upon 
the  student?  Are  we  justified  in  sacrificing  quantity 
to  quality?  Not  a  few  say  yes.  But  student,  teacher, 
and  community  are  likely  to  hold  that  we  are  not.  On 
the  other  hand,  the  feeling  is  or  should  be  just  as  strong 
that  we  are  not  justified  in  sacrificing  quality  to  mere 
quantity.  We  must  have  both.  How  can  we  get  them? 
Perhaps  the  most  satisfactory  answer  to  this  question 
is  that  we  should  select  from  the  mass  of  material  to  be 
assimilated  in  each  subject  the  important  nodes  of  thought, 
and  subject  these  to  scientific  treatment.  By  so  doing 
we  shall  reduce  to  manageable  proportions  the  amount 
of  subject-matter  that  is  to  be  treated  according  to  scien- 
tific method.  These  nodes  of  thought  are  at  once  the  cen- 
tral conceptions  to  which  everything  else  can  be  related, 
hence  assimilated  and  remembered,  and  the  starting- 
points  for  future  developments.  This  procedure  is  well 
known  and  freely  followed  in  biology,  especially  in  the 
field  of  dissection.  The  mass  of  material  available  for 
this  exercise  is  utterly  unmanageable  when  the  time  of 
the  student  is  considered.  Could  he  live  for  a  thousand 
years  and  devote  all  his  time  to  this  exercise,  he  could  per- 
haps make  a  detailed  dissection  of  most  of  the  available 


EDUCATIONAL    STATUS    OF    HIGH- SCHOOL    STUDENTS       71 

forms  of  plant  and  animal  life,  but  living  for  a  much 
shorter  period,  and  being  able  to  devote  but  a  fraction  of 
his  study  for  a  brief  term  of  years  to  such  pursuits,  he  is 
compelled  to  select  a  few  types  considered  to  be  most 
representative  of  the  forms  that  might  be  studied  in  this 
way. 

What  is  recognized  to  be  a  necessity  in  biology  becomes 
an  opportunity  in  all  other  subjects.  In  every  department 
of  learning  these  pivotal,  developing  nodes  of  thought 
exist,  and  may  be  seized  upon  by  the  teacher  as  a  means 
of  enriching  and  fructifying  the  older  methods  of  teaching 
by  the  infusion  of  those  newer  processes,  which,  patterned 
after  the  efforts  of  the  outside  world  in  its  struggle  with 
real  situations,  are  consequently  full  of  vigor  and  vitality. 

The  important  nodes  of  thought  are  more  easily  dis- 
cerned in  some  subjects  than  in  others.  In  mathematics 
they  are  distinct  and  almost  unmistakable,  yet  so  much 
room  for  improvement  is  there  even  in  arithmetic,  algebra, 
and  geometry  that  more  than  a  score  of  mathematical 
societies  among  high-school  teachers  are  making  the  teach- 
ing of  these  subjects  among  the  most  progressive  educa- 
tional movements  of  the  day.  In  physics  and  chemis- 
try typical  experiments  are  worked  out  in  scientific  form, 
and  made  the  nuclei  about  which  are  clustered  all  the  facts 
and  laws  furnished  by  text-books  and  lectures  in  these 
subjects.  By  common  consent  high-school  English  leads 
all  other  secondary  subjects  in  the  poverty  of  its  results, 


72  SCIENTIFIC    METHOD    IN    INSTRUCTION 

when  the  time  and  effort  devoted  to  it  are  considered 
The  reason  is  that  in  this  subject  the  nodes  of  thought  are 
not  yet  brought  out  and  articulated  into  a  system  that  may 
be  comprehended  and  utilized  by  English  teachers  as  a 
body.  It  is  indeed  dissected  into  spelling,  reading,  com- 
position, grammar,  rhetoric,  and  literature  in  all  its  vari- 
eties, not  to  mention  dictation,  etymological  word  study, 
elocution,  and  dramatization,  but  only  in  the  college  en- 
trance requirements  has  there  been  any  attempt  to  select 
the  typical  portions  even  of  literature,  and  this,  if  one  may 
judge  by  results,  has  been  little  more  than  an  attempt  to 
choose  by  lottery  from  the  unsuitable  as  well  as  the  suit- 
able. German  schoolmen,  on  the  contrary,  have  by  long 
experiment  and  discussion  settled  upon  the  best  types  of 
literature  to  present  in  the  schools,  both  elementary  and 
secondary.1  A  number  of  the  volumes  have  an  appendix  of 
about  a  dozen  pages  each,  giving  the  needful  information 
about  grammar.  Deutsch  with  them  furnishes  a  unified 
course  in  the  mother-tongue,  in  which  the  nodes  of  thought 
are  clearly  distinguishable  and  naturally  related.  Need- 
less to  say,  our  English  must  come  into  the  same  articulate 
form  before  we  shall  be  able  to  get  uniformly  good  results 
from  our  at  present  lavish  expenditure  of  time  and  effort. 
In  history,  nodes  of  thought  may  be  found  in  the  biog- 
raphy of  great  men,  in  selected  periods  of  development, 

1  "Deutsches  Lesebuch,"  10  volumes,  edited  by  Professor  Dr.  Charles 
Muff,  Berlin. 


EDUCATIONAL    STATUS    OF    HIGH-SCHOOL    STUDENTS      73 

in  the  causes,  both  fundamental  and  accessory,  that  have 
determined  events.  Here,  as  elsewhere,  each  node  fur- 
nishes problems  to  be  solved,  and  hence  gives  ample  oppor- 
tunity for  the  application  of  hypothesis  and  its  verifying 
test.  Geography  easily  falls  into  the  type  form  of  study,  as 
do  treatises  that  pertain  to  transportation,  manufacture, 
and  agriculture.1  Similarly,  the  world  of  conceptions, 
whether  as  art,  science,  psychology,  ethics,  or  philosophy, 
has  easily  distinguishable  nodes  of  thought  which  may 
be  selected  by  the  teacher  as  types  for  the  application  of 
scientific  method. 

DISCUSSION  :  —  Examples  of  thought-nodes  from  each  high- 
school  study. 

46.  The  third  point  in  the  educational  status  of  the 
high-school  student  concerns  his  efficiency  in  the  use  of 
the  knowledge  acquired.  A  detailed  exposition  of  the 
value  of  this  aspect  of  high-school  instruction  is  made  in 
Chapter  VII  of  this  book.2  Not  only  should  the  student 
gain  a  clear  insight  into  the  intellectual  achievements 
of  the  race,  but  he  should  also  acquire  the  power  to  use 
effectively  the  ideas  thus  gained.  Efficiency  is  always 
the  correlative  of  insight.  To  paraphrase  Kant,3  insight 

1See  Charles  A.  McMurry,  "Type  Studies  in  Geography,"  The 
Macmillan  Co.  See  also  modern  texts  in  biology. 

2  See  also  "Principles  of  Secondary  Education,"  Vol.  I,  "The  Stud- 
ies," pp.  162-172,  203,  204. 

3  "  Gedanken  ohne  Inhalt  sind  leer,  Anschauungen  ohne  Begriffe  sind 
blind,"  in  "  Kritik  der  reinen  Vernunft,"  p.  79. 


74  SCIENTIFIC    METHOD    IN    INSTRUCTION 

without  efficiency  is  helpless;  efficiency  without  insight  is 
aimless.  Method  in  teaching  must  therefore  always  keep 
this  aspect  of  the  subject  in  mind.  The  investigator  needs 
no  such  admonition,  for  he  gains  efficiency  through  his 
research.  The  student,  however,  is  confronted  with  a 
double  difficulty;  for,  on  the  one  hand,  his  researches  are 
numerous  and  quickly  made,  so  that  the  time  and  repe- 
tition needed  for  gaming  a  high  degree  of  efficiency  are  de- 
nied him,  while,  on  the  other  hand,  he  must  acquire  large 
amounts  of  knowledge  without  even  the  form  of  research. 
Yet  he  should  become  reasonably  efficient  in  the  use  of  all 
that  he  learns.  It  is  for  these  reasons  that  a  good  method 
of  instruction  always  makes  provisions  for  acquiring 
practical  efficiency  in  the  use  of  knowledge. 

With  these  preliminary  reflections  concerning  the  exist- 
ing differences  between  the  high  school  and  the  outside 
world,  we  may  now  pass  to  a  consideration  of  those  grand 
divisions  in  the  realm  of  method  that  have  in  varying  degree 
always  been  the  tools  of  the  man  who  would  know. 


CHAPTER   V 
THE  INDUCTIVE  APPROACH 

47.  Logicians  have  long  since  recognized  that  there 
are  two  leading  methods  of  approach  to  knowledge  and 
insight,  namely,  the  inductive  and  the  deductive,  though 
neither  of  these  methods  is  often  used  independently  of 
the  other.1 

1  German  Herbartians  defend  their  so-called  'Formal  Steps'  as  a 
complete  method,  since  it  recognizes  both  inductive  and  deductive  stages. 
Critical  examination,  however,  shows  that  'deduction'  as  they  use  the 
term  is  confined  to  the  'application'  of  knowledge  inductively  ac- 
quired in  a  given  lesson.  They  fail  to  recognize  that  the  deductive 
approach  is  equally  useful  in  the  acquisition  of  knowledge.  Why  should 
one  go  on  storing  up  generalizations  by  inductive  approach,  if  the  prin- 
ciples thus  acquired  are  to  be  of  no  use  in  gaining  new  knowledge,  in 
explaining  the  reasons  for  things?  Otherwise  one  would  be  shut  up  to 
the  necessity  of  demonstrating  anew  every  principle  of  explanation  when- 
ever the  occasion  for  its  use  should  arise.  Are  the  demonstrations  of 
geometry  not  to  be  of  use  in  solving  new  problems?  Must  the  fun- 
damental laws  of  motion,  mechanics,  heat,  light,  and  electricity  never  be 
used  to  explain  phenomena,  except  as  they  are  derived  anew  by  induc- 
tive approach?  Were  that  the  case,  one  could  never  give  a  child  a  reason 
for  a  thing,  without  subjecting  him  to  an  inductive  process.  Shall  we 
banish  the  word  because  from  our  vocabulary?  Deductive  reasoning, 
however,  is  applied  whenever  this  word  is  used.  Why  does  water  rise 
in  the  pump?  Because  of  the  inequality  of  air  pressure  inside  and  out- 
side of  it.  Why  does  the  dew  fall  ?  Because  the  fall  in  temperature 
brings  the  air  below  the  point  of  saturation.  It  is  this  incompleteness 

75 


70  SCIENTIFIC    METHOD    IN    INSTRUCTION 

What  Francis  Bacon  called  the  new  method  is  in  sharp 
contrast  to  the  old  method  of  the  middle  ages,  when  men 
were  concerned  not  so  much  in  establishing  principles  as 
they  were  in  drawing  conclusions  from  admitted  premises. 
The  difficulty  of  using  the  old  method  as  one  of  research 
was  that  it  assumed  or  accepted  from  authority  the  prin- 
ciples from  which  it  reasoned,  whereas  the  greatest  need 
of  the  new  natural  sciences  was  that  all  their  old  principles 
should  be  verified,  and  that  new  ones  should  be  established 
through  inductive  research  by  means  of  observation,  ex- 
periment, hypothesis,  and  analogy.  Bacon  very  properly 
rejected  the  old  deductive  method  as  utterly  impotent  and 
barren  in  the  new  field.  As  we  have  already  seen,1  be 
compared  the  final  causes,  of  which  the  past  had  made  much 
use,  to  vestal  virgins,  worthy  of  reverence  but  unfruitful. 

The  case  for  deduction  as  a  useful  method  in  education 
is  not  so  bad,  however,  as  it  was  in  science  at  the  time  of 
Bacon,  except  for  its  influence  upon  the  student's  general 
attitude  of  mind ;  for,  whereas  in  Bacon's  day  men  did  not 
know  the  laws  of  nature  in  any  adequate  sense,  they  do 
at  present,  at  least  to  the  extent  necessary  for  instructing 
youth.  Therefore,  if  we  now  refrain  in  many  cases  from 
using  this  method,  it  must  be  for  reasons  somewhat  differ- 
in  the  theory  of  the  'Formal  Steps,'  and  perhaps  also  its  tendency  to 
insist  upon  a  fixed  order  of  procedure,  that  have  led  to  the  severe  criticisms 
that  have  been  made  upon  it  in  Germany,  and  that  have  led  in  many 
quarters  to  an  underestimate  of  its  inherent  excellence. 

1 "  Principles  of  Secondary  Education,"  Vol.  I,  p.  61. 


THE    INDUCTIVE    APPROACH  77 

ent  from  those  that  animated  Bacon.  Granted  that  the 
teacher  knows  his  subject,  there  is  now  no  appreciable 
danger  that  he  will  mislead  his  students  just  because  he 
proceeds  by  the  deductive  road.  But  if  a  given  principle  is 
either  unknown  or  wrongly  interpreted,  there  is  nothing 
to  do  but  to  master  it  by  inductive  research.  It  is,  there- 
fore, not  lest  he  teach  a  false  or  undeveloped  science  that 
the  modern  teacher  so  often  treads  the  inductive  path,  but 
because  he  is  persuaded  that  by  using  this  method  he  can 
get  better  results  than  he  can  by  using  the  other.  Some 
of  these  results  have  been  already  sufficiently  described. 
They  pertain  to  such  things  as  alertness  of  mind,  growing 
interest  in  knowledge  and  its  acquisition,  the  ways  of  testing 
and  of  taking  the  initiative  in  finding  out  the  truth,  vivid- 
ness of  perception,  depth  of  insight,  hospitality  toward 
new  problems  and  eagerness  to  solve  them.  These  are 
all  valuable  as  mental  acquisitions,  and  if  the  use  of  induc- 
tive methods  will  help  to  bring  them  about,  the  time  will 
not  be  wasted  that  is  used  to  master  its  ideals  and  processes. 
The  immediate  purpose  of  induction  is,  of  course,  the 
derivation  of  a  rule  or  principle,  the  establishment  of  a 
class,  or  the  disco  very  of  a  cause  or  effect.  In  other  words, 
the  goal  of  an  induction  is  a  generalization,  a  classification, 
or  a  causal  relation.  What  is  true  of  an  induction  to  the 
investigator  holds  likewise  in  the  high  school,  subject  to 
the  modifications  brought  about  by  the  educational  status 
of  the  student,  as  above  described. 


78  SCIENTIFIC    METHOD    IN    INSTRUCTION 

48.  According  to  the  foregoing  analysis  there  are  at 
least  three  plainly  marked  stages  in  all  educational  methods 
that  aspire  to  scientific  completeness.  They  are  as  fol- 
lows :  — 

1.  The  acquisition  of  facts  by  means  of  authority, 
observation,  and  experiment. 

2.  The  determination  of  the  meaning  of  these  facts 
through  the  processes  of  reasoning. 

3.  The  development  of   efficiency  in  the  use  of  the 
knowledge  so  acquired. 

Looking  at  these  three  stages  from  the  standpoint  of 
the  mental  processes  involved,  we  may  rename  them  as 
follows:  — 

1.  Processes  of  Apperception.      A  fact  is  not  acquired 
until  it  is  apperceived,  i.e.,  brought  into  conscious  relation 
to  other  related  elements  of  what  is  known  by  the  student. 

2.  Processes  of   Thought.     Thinking  is  necessary  in 
determining  the  meaning  of  facts,  in  explaining  the  sig- 
nificance of  things  and  events.    It  completes  the  mental 
assimilation  begun  when  the  facts  are  acquired. 

3.  Processes  of  Application.      A  student  is  not  effi- 
cient in  the  use  of  knowledge  until  he  has  had  a  large 
amount  of  practice  in  applying  it  to  new  situations.    Each 
of  these  three  fundamental  categories  holds  for  both  deduc- 
tive and  inductive  methods,  and  may  now  be  taken  up 
in  detail  and  examined  from  the  standpoint  of  the  induc- 
tive approach. 


THE    INDUCTIVE    APPROACH  79 


I.  Processes  of  Apperception  —  Induction 

49.  The  initial  stage  in  the  acquisition  and  assimilation 
of  facts  leading  to  an  induction,  whether  they  be  obtained 
through  authoritative  transmission,  observation  alone,  or 
observation  directed  and  controlled  by  experiment,  is  a 
clear  and  definite  formulation  of  the  end,  aim,  or  purpose 
of  the  lesson  to  be  learned.  This  problem,  end,  or  aim 
in  induction  is  the  establishment  of  one  or  another  of  the 
three  leading  goals  of  inductive  research,  namely,  a  cause 
(or  effect),  a  classification,  or  a  generalization.  There 
may,  of  course,  be  many  intermediate  lessons  upon  the 
stages  that  lead  to  the  final  general  truth,  such  as  those  that 
pertain  to  the  mastery  of  facts  given  by  authority,  say  in 
books,  the  direct  observation  of  physical  phenomena, 
the  performance  of  experiments  for  the  discovery  or  con- 
firmation of  facts,  etc.,  but  neither  student  nor  teacher 
should  forget  that  these  stages  are  but  contributory  to 
the  main  solution  of  the  problem.  In  order  to  make  this 
formulation  of  end,  aim,  or  purpose,  it  is  often  necessary 
to  take  some  liberties  with  the  presentations  given  in 
text-books,  for  it  is  usually  the  case  that  they  fail  to  throw 
into  bold  relief  the  essential  nodes  of  thought.  In  history, 
for  example,  the  main  concern  of  the  author  of  a  text-book 
usually  appears  to  be  to  get  everything  in.  To  all  appear- 
ances he  first  makes  a  schematic  catalogue  of  all  the  facts, 


80  SCIENTIFIC    METHOD    IN    INSTRUCTION 

and  then  writes  it  up,  contracting  the  treatment  of  the 
topics  he  fain  would  enlarge  upon  in  order  that  nothing 
may  be  omitted.  This  is  perhaps  the  worst  possible  way 
of  presenting  the  subject  to  the  student,  for  the  thing  that 
interests  him,  making  the  subject  seem  worth  while,  is  an 
intensive  and  extensive  study  of  the  nodes  of  history,  that 
is,  the  crucial  events,  the  far-reaching  principles  at  stake 
in  a  given  situation,  the  basal  causes  of  great  national 
activities.  For  such  treatment  of  historical  subjects  we 
must  go  to  the  monograph  on  the  one  hand,  and  on  the 
other,  to  the  monumental  works  in  which  genius  has  op- 
portunity to  reveal  its  insights  in  due  proportion.  An 
illustration  of  the  ideal  historical  monograph  is  that  by 
F.  J.  Turner  on  "The  Significance  of  the  Frontier  in 
American  History."  *  This  gives  an  adequate  exposition 
of  thought-nodes  which  have  an  inherent  value  and  an 
important  development.  It  treats  in  succession  the  In- 
dian trader's  frontier,  the  rancher's  frontier,  the  farmer's 
frontier,  showing  how  each  succeeding  one  developed  out 
of  the  earlier,  and  the  reflex  influence  of  each  upon  those 
that  were  earlier  in  time,  and  farther  east  in  geographical 
location.  It  traces  the  dominating  influence  of  these  va- 
rious frontiers  upon  the  land  policy  of  the  United  States 
in  its  disposition  of  the  public  domain,  a  policy  that  always 

1  Annual  Report  of  the  American  Historical  Society  for  1893,  pp.  199- 
227;  also  the  Fifth  Year-Book  of  the  National  Herbart  Society,  Univer- 
sity of  Chicago  Press. 


THE    INDUCTIVE    APPROACH  8l 

astonishes  the  European;  it  shows  in  illuminating  fashion 
how  the  needs  and  demands  and  power  of  these  same 
frontier  regions  have  dominated  our  tariff  laws  and  our 
policy  of  internal  improvements,  from  the  early  building 
of  turnpikes,  railroads,  and  canals  to  our  latest  schemes 
for  reclaiming  land,  both  from  too  little,  and  too  much 
water.  The  first  cry  was  "bring  the  farm  to  the  factory" 
by  developing  means  of  transportation,  which  was  done; 
its  second  demand  was  "bring  the  factory  to  the  farm"  by 
levying  protective  tariffs,  and  this  was  done.  The  mono- 
graph further  reveals  to  the  student  that  the  frontier  is 
the  place  where  the  fusing  of  European  immigrants  into 
a  new  and  composite  nationality  has  taken  place,  and  where 
democracy  and  the  American  spirit  have  been  developed. 
All  this  is  real  American  history,  but  it  is  not  found 
in  text-books. 

Another  illustration  of  the  historian  unbound  is  John 
Fiske,  in  his  "Civil  War  in  the  Mississippi  Valley."  John 
Fiske's  text-book  in  American  history  is  like  all  the 
rest  —  it  has  so  much  in  it  that  there  is  little  in  it  for 
the  student.  But  in  "  The  Civil  War  in  the  Mississippi 
Valley"  the  historian  is  free  to  develop  the  essential  and 
to  suppress  the  insignificant.  A  student  who  reads  this 
volume  thoughtfully,  and  has  time  and  opportunity  to  dis- 
cuss its  salient  points  will  know  more  about  the  Civil  War 
in  the  West,  and  will  develop  a  keener  interest  in  historical 
subjects  than  he  would  get  by  studying  a  dozen  text-books 


82  SCIENTIFIC    METHOD    IN    INSTRUCTION 

on  the  subject.  What  is  true  in  history  holds  in  due  meas- 
ure of  all  the  other  high-school  subjects,  and  this  fact  has 
an  important  bearing  upon  how  the  work  should  be  di- 
vided and  the  aim  of  the  lesson  determined. 

(i)  Setting  the  Problem 

50.  It  is  a  function  of  special  didactics  to  search  out  and 
set  in  order  in  the  respective  subjects  the  important  nodes 
of  thought  that  should  be  studied  according  to  scientific 
methods.1  Each  of  these  gives  rise  to  one  or  more  problems 
proper,  and  usually  to  a  number  of  subsidiary  aims.  For 
instance,  in  the  case  of  the  frontier  the  main  problem 
before  the  class  would  be  to  determine  the  influence  of 
the  frontier  in  American  history.  About  this  problem  will 
cluster  the  gathering  of  historical  facts,  the  influences 
that  have  a  causal  power,  and  the  various  channels  through 
which  these  causes  produce  their  diverse  effects.  In  other 
words,  the  main  problem  will  break  up  into  a  number  of 
subsidiary  ones,  as,  for  example,  what  influence  had  the 
trapper's  frontier  upon  that  of  the  rancher  ?  What  modi- 
fying influences  had  the  settlements  immediately  beyond 
the  '  fall  line '  upon  those  below  it  ?  How  did  the  frontier 
regions  control  legislation  for  internal  improvements  ?  for 
the  distribution  of  the  public  domain?  for  protection  to 
new  industries,  etc.  ? 

'"Principles  of  Secondary  Education,"  Vol.  I,  "The  Studies,"  pp. 
162-172,  203,  204. 


THE    INDUCTIVE    APPROACH  83 

Problems  for  inductive  lessons  always  grow  out  of  the 
needs  of  the  student  and  the  nature  of  the  subject-matter. 
There  is  no  excuse  for  an  inductive  lesson  to  develop  that 
which  to  the  student  is  self-evident  or  which  lies  so  near 
at  hand  that  formal  and  laborious  methods  to  attain  it 
become  childish  or  ridiculous.  Large  instruments  should 
be  used  primarily  for  ends  that  are  both  important 
and  difficult  to  attain.  We  do  not  use  sledge-hammers 
to  forge  watchsprings.  It  is  because  of  these  considera- 
tions that  one  should  seek  out  in  every  subject  those  types 
or  nodes  of  thought  whose  mastery  gives  the  student  in- 
sight into  a  whole  series  of  situations,  and  an  easy  and 
effective  control  of  his  own  powers  in  the  domain  in  ques- 
tion. Teaching  is  an  art,  and  hence,  like  all  arts,  is  free. 
This  means  that  such  a  subject  as  English,  for  example, 
may  be  taught  as  an  organic  whole  or  in  correlated  de- 
partments or  divided  up  into  independent  branches.  If 
grammar  is  to  be  an  isolated  study  for  a  series  of  months, 
it  will  give  rise  to  a  set  of  problems,  to  master  which  by 
inductive  study  will  result  in  easy  and  complete  mastery 
of  the  whole  field.  Nor  are  these  problems  numerous  or 
exceedingly  difficult  for  the  high-school  student.  In  ety- 
mology we  have  such  nodes  as  the  nature  and  classifica- 
tion of  nouns  and  pronouns,  the  nature  and  internal 
modification  of  the  verb,  the  nature  and  forms  of  the 
adjective,  the  adverb,  and  of  conjunctions,  both  coordinate 
and  subordinate.  Syntax,  in  like  manner,  has  its  problems 


84  SCIENTIFIC    METHOD    IN    INSTRUCTION 

of  construction,  of  concord  and  government,  of  coordina- 
tion and  subordination,  arrangement,  position,  etc.  Lit- 
erature always  has  its  problems  to  solve,  whether  they 
refer  to  words,  structure,  personality,  form,  content,  plot, 
character,  style,  motive,  movement,  or  what  not. 

The  problem  lies  close  at  hand  in  all  the  natural  sciences, 
some  of  which,  as  in  physics,  call  for  the  inductive  estab- 
lishment of  generalizations  in  the  form  of  laws  and  prin- 
ciples, some  deal  with  classification,  as  in  biology,  and  others 
involve  largely  the  investigation  of  cause  and  effect.  In 
short,  whenever  it  is  worth  while  to  lead  the  student,  by 
the  inductive  road,  to  a  comprehension  and  mastery  of 
any  general  truth,  the  inductive  problem  is  involved,  and 
should  be  recognized  and  formulated  accordingly. 

DISCUSSION  :  —  Kind  of  problems  that  are  fitting  for  induc- 
tive treatment l  in:  i.  foreign  languages;  2.  English;  3.  his- 
tory; 4.  algebra;  5.  geometry;  6.  physics;  7.  chemistry; 
8.  physical  geography. 

1  See  the  respective  volumes  on  special  didactics  issued  in  one  series 
by  The  Macmillan  Co.,  and  in  another  by  Longmans,  Green,  &  Co., 
both  of  New  York.  The  titles  are  as  follows  :  — 

A.  The  Macmillan  Co.     i.  "The  Teaching  of  Elementary  Mathe- 
matics," David  Eugene  Smith.    2.  "  The  Teaching  of  English,"  Percival 
Chubb. 

B.  Longmans,  Green,  &  Co.       i.  "The    Teaching    of    Latin   and 
Greek,"  Bennett  and  Bristol.      2.  "The  Teaching  of  English,"  Car- 
penter,   Baker    and   Scott.      3.  "The    Teaching    of    Chemistry    and 
Physics,"  Smith  and  Hall.     4.  "  The  Teaching  of  History  and  Civics," 
Henry  E.  Bourne.      5.  "The  Teaching  of   Mathematics,"  J.   W.  A. 
Young.     6.  "  The  Teaching  of  Biology,"  Lloyd  and  Bigelow. 


THE    INDUCTIVE    APPROACH  85 

(2)  Acquiring  the  Facts 

51.  Two  questions  at  once  arise  when  this  topic  is 
treated:  (i)  what  facts  are  needed  for  an  induction? 
and  (2)  how  are  they  to  be  acquired? 

How  many  and  what  kind  of  facts  should  be  acquired 
to  make  an  induction?  If  the  induction  were  to  be  ac- 
cepted without  test  as  final,  we  should  in  non-mathe- 
matical inductions  need  to  be  sure  of  practically  all  of 
the  facts,  for  our  conclusion  would  always  be  subject  to 
disturbance  by  some  unsuspected  incongruence  between 
our  thought  and  the  facts.  But  since  inductions  pass 
through  the  stages  of  hypothesis  and  verification,  it  is 
safe  to  begin  to  generalize  as  soon  as  we  seem  to  have  a 
warrant  for  doing  so.  Thus  in  the  case  of  the  death's- 
head  moth  above  mentioned,  a  single  observation  con- 
vinces us  that  there  must  somewhere  be  more  of  them, 
and  that  as  a  class  they  will  have  these  peculiar  markings. 
It  will  be  seen  that  in  this  case  an  induction  is  made  from 
a  single  observation.  In  Porto  Rico  there  is  a  destructive 
creature  with  a  puckery  little  face,  like  a  microscopic 
edition  of  the  weazened  countenance  of  an  old-time  Euro- 
pean diplomat  as  he  is  usually  pictured,  the  wings  and 
body  of  a  beetle,  the  hind  legs  of  a  grasshopper,  and  the 
burrowing  claws  of  a  mole.  He  flies  to  his  pasture  and 
burrows  in  the  ground  to  feed  on  the  tender  roots  of  plants. 
How  shall  such  a  creature  be  classified,  and  what  is  his 


86  SCIENTIFIC    METHOD    IN    INSTRUCTION 

English  name?  His  Spanish  name  is  Changa,  but  that 
gives  us  no  idea  of  his  real  place  in  the  insect  world.  Our 
first  task  is  to  locate  this  fellow  in  the  general  class  of  insects 
to  which  he  belongs;  comparing  him  with  the  two  classes 
to  which  he  seems  most  akin,  namely,  the  crickets  and  the 
grasshoppers,  we  shall  find  that  he  undoubtedly  belongs 
to  the  cricket  family,  since  the  most  of  his  characteristics 
place  him  there.  The  query  next  arises,  is  he  a  new  variety  ? 
or  are  there  other  known  crickets  that  have  the  burrowing 
claw?  Examination  of  specimens  or  of  pictures  of  such 
show  that  there  is  a  class  of  insects  in  the  United  States 
having  these  claws,  and  that  they  are  called  mole  crickets. 
Undoubtedly,  therefore,  our  little  friend,  or  enemy  if  we 
like,  belongs  in  this  class.  At  least  it  is  safe  to  place  him 
there  temporarily.  In  the  case  of  classification,  therefore, 
we  may  make  our  tentative  induction  with  any  convenient 
number  of  pertinent  facts. 

Were  the  problem  an  inductive  study  of  the  barometer, 
we  should  need  facts  about  the  weight  of  quicksilver  and 
of  water,  and  should  need  to  know  that  the  air  presses  with 
a  considerable  weight  upon  all  objects  at  the  surface  of 
the  earth.  We  should  also  need  to  know  how  a  column  of 
mercury  or  of  water  can  be  relieved  of  air  pressure  on  its 
top ;  that  is,  we  should  understand  the  nature  of  a  vacuum 
and  how  it  can  be  produced.  If  our  problem  extends  to 
the  uses  of  the  barometer,  we  should  need  facts  also  about 
how  changing  weights  of  air  pressure  are  brought  about. 


THE    INDUCTIVE    APPROACH  87 

With  such  facts  as  these  at  hand  we  should  be  able  to  de- 
rive causes  and  principles  concerning  the  barometer  and 
its  uses.  With  all  such  topics,  the  nature  of  the  sub- 
ject-matter determines  what  kind  of  facts  are  essential 
to  a  proper  induction. 

If  the  problem  were  to  determine  the  effects  of  the 
invention  of  the  cotton-gin  upon  the  development  of 
slavery,  the  facts  necessary  would  relate  not  only  to  the 
invention  itself,  but  to  contributory  conditions  north  and 
south,  such  as  climate,  soil,  political  and  social  ideals,  and 
manufacturing  facilities.  To  seek  to  understand  a  great 
economic  and  social  condition  such  as  slavery  from  the 
examination  of  a  single  cause,  irrespective  of  its  attendant 
conditions,  would  be  to  arrive  at  valueless  conclusions,  and 
to  lead  to  bad  methods  of  study  at  the  same  time. 

Should  the  problem  be  to  make  an  inductive  study  of 
a  character  in  literature,  say  Macbeth,  needful  facts 
would,  as  Bain  *  points  out,  be  such  as  pertain  (i)  to  the 
physical  make-up  of  the  man;  (2)  the  physical  treatment 
of  the  system,  as  to  food,  drink,  exercise,  as  influenced  by 
health,  economic  status,  occupation,  etc.;  (3)  the  natural 
and  social  surroundings  as  they  affect  the  mind,  whether 
the  people  are  cultured  or  rude,  rural  or  urban  (witches), 
the  landscape  rugged  or  even,  fertile  or  barren;  (4)  modes 
of  industry  or  habitual  occupation,  as,  for  example,  whether 
the  man  is  a  soldier,  a  sailor,  a  merchant,  a  manufacturer, 

1  "Logic-Induction,"  p.  289. 


88  SCIENTIFIC    METHOD    IN    INSTRUCTION 

a  farmer,  or  a  priest;  (5)  the  status  of  the  society  in  which 
the  man  lived;  (6)  the  education  he  has  had,  and  the 
like.  These  and  similar  facts  need  to  be  taken  into  con- 
sideration in  such  a  study. 

In  so-called  mathematical  inductions  the  facts  needed 
are  sufficient  concrete  illustrations  to  bring  the  principle 
in  question  home  to  the  mind  with  clearness  and  convinc- 
ing force  as  to  its  validity. 

To  a  teacher  used  to  the  inductive  method  of  approach 
to  a  problem,  the  determination  of  the  kind  and  number 
of  facts  needful  is  not  a  difficult  matter,  since  the  nature 
of  the  subject  and  problem  practically  settle  these  points. 

DISCUSSION  :  —  Facts  needed  for  specific  cases  of  induction 
in  the  various  studies. 

52.  More  important  than  the  inquiry  into  the  kind  and 
number  of  facts  necessary  or  desirable  for  an  induction 
is  the  second  consideration,  How  are  they  to  be  acquired  ? 
Shall  it  be  by  authority  or  observation  or  experiment? 
Here  we  come  face  to  face  with  the  fatal  facility  of  text 
and  teacher  to  tell,  not  only  the  facts,  but,  alas,  also  the 
causes,  the  effects,  the  classifications,  and  the  generaliza- 
tions. What  chance  has  teacher  or  student  to  escape  this 
inundation  of  narration?  What  incentive  has  either  to 
do  any  real  thinking?  Even  in  the  sciences  supposed  to 
be  the  most  fruitful  in  observation,  description,  and  ex- 
position, the  text-books  tell  the  student  everything  he  will 
find  if  he  looks.  But  having  been  told,  why  should  he 


THE    INDUCTIVE    APPROACH  89 

look?  Curiosity  is  killed  before  it  is  born,  and  natural 
interest  is  dampened  or  extinguished.  The  case  is  more 
hopeful  in  physics  and  chemistry,  where  the  experiment 
is  regarded  as  an  essential  element  in  the  instruction,  even 
when  over-willing  authority  insists  in  telling  the  student 
what  to  look  for,  and  what  he  will  find.  History,  geog- 
raphy, literature,  grammar,  and  biology  suffer  most  from 
the  telling  dementia.  Often,  however,  if  the  teacher  would 
even  temporarily  throw  not  only  physic,  but  the  text- 
book to  the  dogs,  the  situation  for  induction  might  be 
redeemed.  With  a  few  good  monographs  to  indicate  his- 
torical problems,  and  a  few  standard  treatises  like  those 
of  John  Fiske,  Goldwin  Smith,  McMaster,  Von  Holtz, 
not  to  speak  of  Parkman,  Bancroft,  Motley,  and  other 
older  historians,  to  supply  data,  an  inductive  study  of  a 
problem  in  history  may  be  carried  through  so  as  greatly 
to  enhance  knowledge  and  interest.  A  library  is  at  least 
as  good  a  place  as  an  herbarium  for  the  student  to  find 
out  facts  for  himself.  To  be  sure,  the  facts  of  history  are, 
in  a  sense,  given  to  us  at  second  hand,  for  we  live  now,  and 
not  then ;  but  for  all  this  they  lose  little  of  their  freshness 
when  found  as  the  result  of  search.  It  is  only  when  they 
are  deluged  upon  us  without  our  volition  or  desire  or  exer- 
tion that  we  lose  interest  in  them. 

The  older  botanies  were  almost  purely  descriptive, 
telling  all  the  facts  and  principles;  more  recent  ones  have 
added  plant  dissection  with  and  without  the  microscope, 


90  SCIENTIFIC    METHOD    IN    INSTRUCTION 

in  order  to  get  at  the  facts  of  structure ;  the  most  recent,  like 
that  of  Bergen,1  add  experiments  practicable  to  enable 
the  student  to  get  first-hand  knowledge  of  function.  Those 
necessary  facts  which  the  student  could  not  get  by  obser- 
vation and  experiment  without  too  great  expenditure  of 
time  are  given  by  authority,  as  before.  A  large  part  of 
the  laboratory  work  in  chemistry  work  and  physics  is  for 
the  determination  of  facts  which  later  are  to  lead  to  induc- 
tions. Many  experiments  are,  of  course,  designed  to  test 
hypotheses. 

If  inductions  in  literature  are  to  be  attempted,  and  the 
problem,  say  the  mediatory  office  of  Portia,  lies  within  a 
given  book,  then  the  facts  are  to  be  sought  out  by  reading 
the  work  itself.  Should  the  problem,  say  the  treatment 
of  the  supernatural  by  Shakespeare,  lie  in  a  series  of 
works,  the  facts  are  to  be  discovered  by  the  student, 
aided  perhaps  by  citations,  in  all  the  works  of  this  author 
which  embody  this  feature  of  literature.  The  main  point 
is  that  they  should  be  found  by  the  student's  own  investi- 
gations, not  be  given  direct  and  unsought  by  teacher  or 
author.  We  may  conclude,  therefore,  that  in  gathering 
the  needful  facts  for  an  induction,  direct  observation  and 
experiment  should  come  first  as  the  royal  means,  to  be 
limited  only  by  the  nature  of  the  subject  and  the  time  at 
disposal;  and  that  in  those  cases  where  the  facts  must 
be  taken  at  second  hand,  either  from  the  nature  of  the 

1  Joseph  Y.  Bergen,  "Elements  of  Botany,"  Ginn  &  Co.,  Boston. 


THE    INDUCTIVE    APPROACH  91 

problem  or  the  necessity  of  getting  over  the  ground,  they 
should  never  be  passively,  but  always  actively  acquired 
by  the  student. 

DISCUSSION  :  —  Practical  limits  to  observation  and  experi- 
ment as  means  for  gathering  facts  in:  i.  languages;  2.  his- 
tory;1 3.  exact  sciences;2  4.  biological  science;8  5.  earth 
sciences. 

2.  Processes  of  Thought — Inductive  Approach 

53.  That  toward  which  we  approach  by  the  inductive 
method  is  some  form  of  generalization,  be  it  a  cause  or 
effect,  a  classification,  a  definition,  a  formula,  or  a  gener- 
alization in  the  form  of  rule,  principle,  or  law.  In  other 
words,  we  are  to  seek  an  adequate  explanation  of  the 
facts  brought  before  us  by  the  problem  in  hand. 

The  essential  thought  stages  of  this  process  are  two; 
namely, 

(1)  The  formation  of  an  hypothesis,  suggested  by  the 
facts  acquired  to  account  for  the  given  phenomenon ;  and 

(2)  The  testing  of  this  hypothesis  by  comparison  of  its 
consequences  with  the  results  of  a  careful  analysis  of  re- 
lated phenomena. 

The  hypothesis  may  turn  out  to  be  correct,  or  as  often 

*Mary  Sheldon  Barnes,  "Studies  in  Historical  Method,"  D.  C. 
Heath  &  Co.,  Boston. 

2  See  Henry  E.  Armstrong,  "The  Teaching  of  Scientific  Method," 
The  Macmillan  Co.,  N.Y. 

3  Compare  Frank  Cramer,  "The  Method  of  Darwin,"  A.  C.  McClurg 
&  Co.,  Chicago. 


92  SCIENTIFIC    METHOD    IN    INSTRUCTION 

happens,  it  may  have  to  be  modified  as  incomplete,  01 
totally  rejected  as  false  or  inadequate.  The  testing  must 
be  continued  until  the  hypothesis  has  proved  to  be  either 
right  or  wrong. 

At  this  point  we  may  see  the  inevitable  mixing  of  methods, 
inductive  and  deductive,  for  the  new  hypothesis  to  which 
we  attain  by  tentative  induction  now  becomes  a  principle 
which  we  proceed  to  test  deductively.  We  do  this  by  de- 
ducing its  consequences  in  a  given  direction,  and  testing 
them  by  known  facts.  Thus,  suppose  we  had  come  by 
inductive  approach  to  the  hypothesis  that  darkness  is  a 
cause  of  dew.  Then  by  this  principle  the  more  darkness 
we  have  the  more  dew  we  should  expect.  But  this  cannot 
be  true,  since  no  dew  falls  in  dark  rooms,  and  it  often  fails 
to  gather  on  the  darkest,  namely,  the  cloudiest  nights. 
This  mixing  of  processes,  however,  need  not  lead  to  con- 
fusion of  thought  by  either  student  or  teacher,  since  it 
arises  so  spontaneously  that  no  attention  need  be  paid 
to  it,  except  for  purposes  of  clear  analysis.  The  essential 
things  to  bear  in  mind  in  the  inductive  approach  have 
already  been  indicated :  —  the  formulation  of  a  clear  aim 
in  the  guise  of  a  problem,  the  gathering  of  pertinent 
facts,  the  tentative  hypothetical  solution  of  the  problem 
suggested  by  the  facts  at  hand,  and  then  a  thorough 
testing  of  the  validity  of  this  hypothesis  by  comparison 
of  its  consequences  with  other  related  facts  which  think- 
ing brings  to  light. 


THE    INDUCTIVE    APPROACH  93 

(i)  The  Hypothesis 

54.  It  sometimes  happens  that  the  mind  leaps  almost 
instinctively  to  the  true  cause  of  a  phenomenon  as  soon  as 
the  needful  facts  about  it  have  been  gathered  and  fairly 
understood,  as  in  the  explanation  of  the  action  of  the  com- 
mon pump  in  consequence  of  its  valves  and  the  outside 
pressure  of  the  atmosphere  upon  the  surface  of  the  water. 
In  such  cases  there  need  be  no  coquetting  with  hypotheses 
and  their  verifications.  The  principle  should  be  frankly 
accepted  as  true  as  soon  as  it  appeals  irresistibly  to  the 
mind,  and  then  its  manifold  applications  illustrated.  It 
is  especially  for  such  cases  as  these  that  Mill's  five  prin- 
ciples concerning  agreement  and  difference  apply  directly 
and  with  convincing  force.1  Their  greatest  field  of  appli- 
cation is  in  the  exact  sciences,  but  they  hold  also  concern- 
ing some  things  in  biological  and  earth  sciences  like  geog- 
raphy and  geology,  as  well  as  in  some  aspects  of  human 
affairs. 

In  most  cases,  however,  in  which  inductive  processes 
are  desirable,  this  early  convincing  certainty  as  to  the  prin- 
ciple of  explanation  is  not  present,  and  the  mind  may  be 
long  in  doubt  as  to  what  is  the  true  explanation.  This 
is  the  case  in  real  life,  for  it  is  only  in  comparatively  recent 
times  that  satisfactory  explanations  have  been  found  for 
seemingly  simple  things,  like  the  falling  of  dew,  the  burn- 

1  Compare  pp.  48-54. 


94  SCIENTIFIC    METHOD    IN    INSTRUCTION 

ing  of  wood,  the  circulation  of  water,  the  glacial  deposit  of 
boulders,  etc.  Even  if  the  modern  schoolboy  is  able  with 
the  aid  of  his  books  and  his  teachers  to  make  short  cuts 
to  race  achievement,  he  should,  nevertheless,  be  trained 
in  the  forms  of  thought  that  have  led  to  these  results, 
and  will  lead  to  like  ones  hereafter. 


(2)  Cause  and  Effect 

55.  The  form  of  the  hypothesis  will,  of  course,  follow 
the  solution  called  for  by  the  nature  of  the  problem. 
In  history  and  in  some  departments  of  natural  science  it 
will  call  for  either  prediction  as  to  cause  or  effect,  or  both. 
Were  the  problem,  What  was  the  effect  of  English  home 
politics  upon  English  colonial  policy  at  the  time  of  the 
Revolution?  the  facts  gathered  and  the  hypotheses  de- 
vised would  pertain  first  to  causes,  and  then  the  deductive 
prediction  as  to  their  probable  effect.  In  similar  fashion, 
the  problem  may  be  to  determine  the  influence  of  circum- 
stances upon  two  historical  characters,  one  of  whom  ap- 
pears to  have  been  moulded  by  them,  while  the  other 
seems  to  have  controlled  them  for  his  own  purposes.  The 
hypothesis  is  in  place  here,  even  though  it  is  as  shifting  as 
the  flight  of  birds.  Did  this  or  that  contingency  turn 
the  expected  victory  to  defeat?  Yes,  for  the  sleet  storm 
retarded  the  designed  movement  of  troops.  No,  for  there 
were  more  fundamental  reasons,  perhaps  of  a  psychical 


THE    INDUCTIVE    APPROACH  95 

nature ;  the  men  were  discouraged  by  their  losses  and  the 
apparent  hopelessness  of  their  cause.  Again,  how  are 
the  given  facts  to  be  interpreted  ?  Comenius,  for  example, 
aimed  at  a  complete  reformation  of  instruction,  yet  he 
was  known  for  two  hundred  years  merely  as  a  man  with 
a  new  method  of  teaching  Latin.  Why  should  an  incident 
only  of  his  reform  be  heeded?  Shall  the  hypothesis  be, 
say,  because  he  was  a  bishop  ?  because  he  was  visionary  ? 
ahead  of  his  age?  hampered  by  the  convulsions  of  the 
Thirty  Years'  War?  because  his  system  lacked  a  psy- 
chological basis?  Each  of  these  suppositions  may  be 
examined  in  turn,  to  be  either  approved  or  rejected  wholly 
or  in  part. 

Should  the  problem  be  to  find  the  effect  of  a  given  fer- 
tilizer upon  plant  growth,  a  prediction  can  be  made  from 
analogy  with  other  fertilizers,  and  then  the  necessary 
verifying  experiments  be  tried.  Or,  what  is  more  probable, 
the  experiment  will  be  tried  first,  a  conclusion  as  to  the 
universality  of  such  effects  be  formulated  from  this  one 
trial,  and  then  subsequently  tested  under  new  conditions 
and  with  other  plants. 

Teachers  who  are  desirous  of  treating  at  least  some 
topics  hi  history  by  inductive  methods,  in  which  the 
hypothesis  plays  an  important  part,  will  find  much  aid 
in  the  works  of  such  authors  as  Mary  Sheldon  Barnes,1 

1  "Studies  in  American  History,"  "Studies  in  General  History," 
"Studies  in  Historical  Method,"  D.  C.  Heath  &  Co.,  Boston. 


96  SCIENTIFIC    METHOD    IN    INSTRUCTION 

B.  A.  Hinsdale,1  Albert  Bushnell  Hart,2  and  Edwin 
M.  Bacon.3  Of  all  these  Mrs.  Barnes  is  probably  the 
most  helpful. 

(3)  Classification 

56.  The  high-school  subjects  in  which  inductive  work 
in  classification  is  especially  appropriate,  are  botany, 
zoology,  and  mineralogy.  Bain  even  calls  them  the 
sciences  of  classification,  so  important  is  this  aspect  of 
their  study.  They  are,  moreover,  the  sciences  in  which 
the  getting  of  knowledge  of  facts  at  first  hand  by  obser- 
vation seems  most  necessary  and  natural.  Observation 
and  inductive  classification  are  correlative  processes. 
If  students  are  to  be  led  to  observe,  what  shall  they  do 
with  their  observations  but  condense  them  into  manage- 
able groups  or  classes  as  a  result  of  their  effort  ?  On  the 
other  hand,  if  they  are  to  exercise  the  thought  processes 
involved  hi  classification,  then  the  observations  are  an 
obvious  prerequisite.  Thus,  the  student  begins  the  study 
of  leaves,  say,  with  a  leafy  twig  of  the  elm.  He  makes  a 
sketch  of  it  to  impress  its  form  and  structure  upon  his 
mind,  noticing  how  many  rows  of  leaves  there  are,  how 
much  overlapping  of  leaves  there  is  when  the  upper  sides 

1  "How  to  Study  and  Teach  History,"  D.  Appleton  &  Co.,  N.Y. 

J  "American  History  told  by  Contemporaries,"  The  Macmillan  Co., 
N.Y. 

•  "Historic  Pilgrimages  in  New  England,"  Silver,  Burdett  &  Co., 
N.Y. 


THE    INDUCTIVE    APPROACH  97 

are  held  toward  him;  what  the  shape  of  an  individual 
leaf  is  taken  as  a  whole  and  whether  it  is  bilaterally  sym- 
metrical or  not;  the  shape  at  the  tip,  at  the  base,  or  the 
margin,  etc.  Then  he  makes  a  similar  study  of  the  maple 
leaf,  observing  hi  what  respects  the  veining  and  other 
characteristics  are  like  those  of  the  elm  and  in  what  re- 
spect they  are  different.  Proceeding  in  this  way  until  a 
sufficient  number  of  different  leaves  have  been  minutely 
studied,,  he  is  then  ready  to  group  them  into  classes  accord- 
ing to  striking  characteristics,  such  as  those  that  pertain 
to  veining,  simple  or  compound  structure,  arrangement, 
etc.  In  a  similar  way  he  will  study  stem,  bud,  roots, 
cells,  functions,  and  the  like.  Such  exercises  hi  inductive 
classification  are  of  special  importance  while  the  student 
is  building  up  his  knowledge  of  classes  upon  a  basis  of 
first-hand  experience.  When,  however,  this  initial  knowl- 
edge is  well  established,  he  can  make  free  deductive  use 
of  it  hi  the  study  of  other  plants  that  are  new  to  him. 

All  sciences  of  classification  have  two  aspects ;  the  one 
general,  and  the  other  special.  The  general  aspect  re- 
lates to  species,  genera,  or  larger  grand  divisions;  the 
special  relates  to  the  detail  of  characteristics  belonging 
to  objects,  and  forms  the  descriptive  part  of  the  science. 
Thus  hi  mineralogy,  the  general  divisions  comprise  crystal- 
lography, or  the  form  of  minerals;  the  physical  properties, 
as  cleavage,  fracture,  hardness,  tenacity,  specific  gravity, 
optical  properties,  heat,  electricity,  magnetism;  chemical 


98  SCIENTIFIC    METHOD    IN    INSTRUCTION 

properties,  as  chemical  composition  and  reactions.  The 
special  division,  named  description  of  species,  is  the  de- 
tailed account  of  all  known  minerals  according  to  these 
properties. 

In  botany,  the  first  division  comprises  structural  and 
morphological  botany,  or  the  parts  of  the  plants  generally, 
tissues,  and  organs,  stated  on  the  methodical  plan  of  pro- 
ceeding from  the  general  to  the  special.  Nutritive  organs 
have  precedence  of  the  reproductive;  their  subdivisions 
are  taken  in  the  order,  root,  stem,  leaves.  The  division 
is  completed  by  the  functions  or  physiology  of  the  different 
tissues  and  organs.  In  zoology,  the  same  general  order 
of  procedure  is  followed  out,  though  not  in  so  great  detail 
on  account  of  complications.1 

It  is  the  function  of  the  larger  type  studies  in  biology 
and  mineralogy,  already  described,2  to  enable  the  student 
through  his  own  observation  and  inductive  reasoning  to 
arrive  at  a  first-hand  knowledge  of  the  broader  classifica- 
tions of  the  study.  The  classification  needed  in  the  special 
descriptive  parts  may  be  more  rapidly  attained  through 
speedy  but  accurate  observations. 

There  is  some  classification  necessary  in  grammar,  such 
as  that  of  nouns  and  pronouns  and  the  other  parts  of  speech ; 
but  the  inductive  approach  to  these  matters  is  mostly 
made  in  the  elementary  school,  and  has,  moreover,  no 

1  Compare  Bain,  "Logic-Induction,"  pp.  184,  185. 

2  See  pp.  57,  58;  see  also  Section  45. 


THE    INDUCTIVE    APPROACH  99 

such  educational  value  or  practical  usefulness  as  classifica- 
tion in  the  biological  sciences. 

DISCUSSION  :  —  Examples  of  inductive  approach  to  classi- 
fications in  zoology;  in  mineralogy. 

(4)  Generalization 

57.  In  former  sections  (39-42)  the  meaning  and  func- 
tion of  the  generalization,  both  mathematical  and  non- 
mathematical,  as  a  stage  in  scientific  explanation,  have 
been  discussed.  Where  the  inductive  derivation  of  a 
generalization  is  the  thought-object  of  a  lesson,  hypotheses 
are  freely  used,  —  to  be  tested  and  amended  or  discarded 
if  found  inadequate,  or  retained  after  sufficient  verifica- 
tion. 

Induction  always  involves  a  leap,  —  a  jump  to  conclu- 
sions lying  beyond  the  cases  under  immediate  observa- 
tion. This  can  be  hardly  called  a  leap  in  the  dark,  how- 
ever, for  back  of  it  is  a  belief  in  the  uniformity  of  nature ; 
that  is,  a  confidence  that  under  uniform  conditions  like 
causes  will  produce  like  effects.  But  the  purpose  of  in- 
ductive lessons  in  the  school  is  not  so  much  to  exercise 
students  in  making  this  leap,  as  to  teach  them  rather  to 
look  both  before  and  after  the  leap  to  see  if  it  is  fully  justi- 
fied by  the  facts.  We  are  all  prone  to  jump  to  conclusions, 
but  we  are  not  all  equally  trained  to  inquire  into  then: 
validity.  Induction  is  one  of  the  world's  important 
methods  of  discovering  the  laws  that  govern  it,  and  the 


ICO  SCIENTIFIC    METHOD    IN    INSTRUCTION 

school  has  not  done  its  full  duty  until  it  has  trained  its 
students  to  use  the  method  effectively  and  safely.  That 
induction  pure  and  simple  is  seldom  used  either  in  school 
or  in  life  is  most  true,  as  will  hereafter  be  made  sufficiently 
clear,  but  there  is  a  distinct  gain  for  exposition  in  consid- 
ering it  as  if  it  were  entirely  independent. 

58.  Writers  on  induction  always  point  out  that  the 
basal  propositions  on  which  all  our  reasoning  rests  are 
inductively  derived  from  our  experience,  originating  in 
the  facts  revealed  by  observation.  This  view  holds  with 
unquestionable  validity  in  the  realm  of  non-mathematical 
generalizations,  whether  they  refer  to  laws  that  govern 
men  or  determine  the  events  of  the  physical  world.  The 
history  of  mathematics  reveals  to  us,  moreover,  that 
many  insights  of  the  mathematician  are  inductively  sug- 
gested, as,  for  instance,  when  the  Egyptians  were  led  to 
develop  geometry  because  geometrical  problems  were 
forced  upon  them  by  the  building  of  the  pyramids  and 
the  annual  inundations  of  the  Nile.  As  Kant  points  out, 
however,  the  generalizations  of  mathematics  when  once 
understood  appeal  to  us  as  universally  valid  and  necessary. 
It  never  occurs  to  us  to  ask  whether  what  is  mathemati- 
cally true  in  the  temperate  regions  is  also  true  in  the  frigid 
zone.  We  know  it  is,  and  we  know,  moreover,  that  it 
was  equally  true  a  million  years  ago  and  will  still  be  valid 
a  million  years  hence.  In  the  biological  world,  however, 
our  inductions  are  not  so  convincing.  Because  all  crows 


THE    INDUCTIVE    APPROACH  IOI 

are  black  in  the  temperate  regions,  we  can  hardly  affirm 
that  they  cannot  be  white  above  the  arctic  circle.  Because 
observation  now  leads  us  to  conclude  that  one  species  does 
not  at  present  arise  from  another,  we  are  not  certain  that 
it  may  not  have  done  so  under  conditions  in  the  past. 
The  position  of  Bacon,  already  mentioned  above,1  that  men 
must  ever  fall  back  upon  constantly  renewed  inductive 
generalizations  to  be  certain  of  their  premises  in  deductive 
reasoning,  still  appeals  to  the  modern  man,  for  it  is  one 
way  of  being  sure  that  generalizations  accord  with  facts. 
The  complementary  method,  is,  of  course,  that  of  veri- 
fication, wherein  a  law  is  applied  to  see  if  it  accords  with 
what  is  already  known.  In  the  words  of  Faraday,  "I 
can  trust  a  fact,  but  I  always  want  to  examine  an  asser- 
tion." 

59.  In  the  experimental  sciences,  like  physics  and 
chemistry,  the  natural  way  is  to  get  at  the  facts  for  an  in- 
duction by  way  of  the  experiment.  Suppose  the  problem 
to  be,  Find  the  law  for  the  intensity  of  light  with  respect 
to  distance.  To  get  at  the  facts,  perform  the  following 
experiment.  In  a  dark  room  place  a  tin  shield  with  a 
small  hole  in  it  in  front  of  a  lighted  lamp;  adjust  a  paste- 
board shield  just  an  inch  square  one  inch  from  and  in 
horizontal  line  with  the  hole  in  the  tin  shield;  rule  a  block 
of  paper  into  inch  squares  and  use  this  to  record  the  size 
of  the  shadow  cast  at  varying  distances  by  the  inch-square 

1  See  pp.  6,  7. 


102  SCIENTIFIC    METHOD    IN    INSTRUCTION 

pasteboard  shield;  move  the  block  of  ruled  paper  back 
until  the  shadow  just  covers  four  squares,  and  measure  its 
distance  from  the  light;  move  the  block  still  further  back 
until  the  shadow  covers  nine  squares,  then  sixteen  squares, 
then  twenty-five,  observing  the  distance  it  has  been  moved 
back  each  time.  What  do  you  find  the  distance  to  be  in 
each  case?  About  one  inch.  Arrange  in  two  lines  the 
two  series,  thus:  — 

Inches  in  distance  from  light  x,  2,  3,  4,     5 

Square  inches  of  shadow  cast  i,  4,  9,  16,  25 

What  relation  do  you  see  between  the  numbers  of  the 
two  series?  Each  of  the  numbers  in  the  second  series 
is  the  square  of  the  corresponding  one  of  the  first.  What 
is  proved  by  the  experiment  ?  That  the  size  of  the  shadow 
cast  is  in  proportion  to  the  square  of  the  distance  from  the 
source  of  the  light.  What  may  be  inferred  about  the  in- 
tensity of  the  light  from  the  same  source  upon  the  spaces 
corresponding  to  the  shadows  were  the  inch-square  paste- 
board screen  removed  ?  The  intensity  of  light  upon  any 
surface  is  inversely  proportional  to  the  square  of  its  dis- 
tance from  the  source  of  light.  Why  ?  Because  the  size 
of  the  shadow  shows  the  amount  of  surface  over  which  a 
given  amount  of  light  would  have  to  be  distributed,  so 
that  the  intensity  of  the  light  is  inversely  proportional 
to  the  square  of  the  distance. 

By  remembering  that  circles  are  to  each  other  as  the 
squares  of  their  diameters,  the  same  results  may  be  ob- 


THE    INDUCTIVE    APPROACH  103 

tained  by  using  a  circular  pasteboard  shield  one  inch  in  di- 
ameter, and  an  unruled  paper  block  to  receive  the  shadow, 
this  time  circular  in  form.  Move  the  block  back  until 
the  shadow  upon  it  is  two  inches  in  diameter,  then  3,  4, 
and  5  inches,  observing  each  time  how  far  back  it  has 
been  moved.  Again  we  get  the  two  series, 

Distance  from  light  i,  2,  3,  4,     5 

Corresponding  size  of  shadow  i,  4,  9,  16,  25 

A  deductive  verification  of  the  result  of  the  induction 
would  be  obtained  by  thinking  of  the  point  of  light  as 
surrounded  by  a  hollow  sphere,  say  i  foot  in  diameter. 
The  ulterior  surface  of  the  sphere  would  receive  all  the 
light,  which  would  fall  equally  upon  it  with  a  certain 
intensity.  Then  suppose  the  first  sphere  removed  and 
another  10  feet  in  diameter  substituted  for  it.  The  same 
light  would  now  have  to  illuminate  a  surface  100  times  as 
great,  hence  the  intensity  would  be  but  y^  as  great  as  in 
the  first  case.  The  surfaces  are  to  each  other  as  100  to  i, 
but  the  distances  of  the  surfaces  from  the  light  are  as  10 
to  i.  Hence  the  law.  (Hoadley's  "Physics,"  p.  377.) 

60.  In  ways  similar  to  those  above  described,  there  may 
be  an  inductive  experimental  approach  to  the  laws  gov- 
erning motion,  velocity,  force,  falling  bodies,  the  pendu- 
lum, the  mechanical  powers,  the  mechanics  of  liquids, 
specific  gravity,  the  various  phenomena  of  sound,  heat, 
and  electricity,  in  short,  to  practically  the  whole  of  physics 
as  taught  in  the  high  school.  Every  good  modern  text 


104  SCIENTIFIC    METHOD    IN    INSTRUCTION 

on  the  subject  abundantly  illustrates  this  procedure  in 
the  experiments  it  recommends.  The  following  abstract 
of  conclusions  reached  by  German  and  French  associa- 
tions show  the  extent  to  which  they  think  work  of  this 
kind  should  be  attempted : *  — 

(1)  In  the  first-year  course  the  method  of  presentation 
is  of  far  greater  importance  than  the  choice  of  subject- 
matter;   i.e.,  it  is  better  to  present  a  few  topics  in  such 
a  manner  that  they  are  powerful  examples  of  the  method 
by  which  science  obtains  its  results,  than  to  try  to  teach 
a  large  number  of  more  or  less  scattered  facts  and  theories 
in   such  a  way  that    they  can  only  be   committed  to 
memory. 

(2)  No  definition  should  be  introduced  until  the  con- 
cepts with  which  it  deals   have   been  clearly  developed 
in  the  student's  mind  by  means  of  a  discussion  of  con- 
crete  cases  from  the   student's   own  world.     In  other 
words,  a  definition  must  be  justified  before  it  is  stated, 
not  after. 

(3)  No  law  should  be  stated  until  the  concepts  and 
relations  with  which  it  deals  have  been  implanted  in  the 
student's  mind  by  means  of  a  discussion  of  common  expe- 
riences and  of  simple  qualitative  demonstrational  experi- 
ments.  After  the  concepts  and  the  ideas  that  there  may  be  a 
quantitative  relation  among  the  factors  involved  have  been 

1  See  School  Review  for  November,  1906,  "A  New  Movement  among 
Physics  Teachers." 


THE    INDUCTIVE    APPROACH  105 

grasped,  the  quantitative  relation  may  be  stated  and 
proved  either  by  demonstration  or  laboratory  experiments. 
In  other  words,  the  student  must  be  given  an  intuitive 
and  qualitative  perception  of  the  relations  summarized  by 
the  law,  before  he  is  expected  to  comprehend  and  use  it 
intelligently. 

(4)  The  student  should  be  made  to  see  clearly  that 
laboratory  apparatus  furnishes  the  means  of  determining 
quantitatively  the  relations  summarized  by  laws.    He 
should  also  be  made  to  see  that  the  apparatus  is  not  the 
law,  that  it  is  not  necessary  to  remember  the  details  of 
the  apparatus  in  order  to  appreciate  the  law,  and  that 
the  exemplifications  of  the  law  are  not  confined  to  the 
apparatus. 

(5)  The  student  should  be  made  to  comprehend  that 
every  law  has  been  established  by  a  method  of  approxi- 
mation, so  that  the  statement  of  law  is  always  a  statement 
of  what  we  believe  to  be  true  in  an  ideal  case.    Hence  the 
measurements  by  which  the  law  is  established  give  results 
which  approach  more  and  more  nearly  to  the  law  the 
more  carefully  the  measurements  are  made,  and  the  more 
completely  complicating  effects  are  eliminated.    He  should 
also  understand  that  in  every  practical  case  the  law  is 
not  verified  because  of  friction,  air  resistance,  etc. 

(6)  Measurements  of  the  relations  involved  in  practical 
cases  lead  to  determinations  of  efficiencies,  rather  than  to 
the  verifications  of  laws.    Such  determinations  of  effi- 


I06  SCIENTIFIC    METHOD    IN    INSTRUCTION 

ciency  furnish  for  the  laboratory  work  problems  which 
are  of  great  value  and  interest  because  of  their  reality. 

DISCUSSION:  —  Illustrations  of  inductive  derivations  of 
generalizations  in  physics. 

61.  Most  modern  works  on  chemistry  use  the  experi- 
ment, not  only  for  determining  facts  and  verifying  laws, 
but  also  for  deriving  inductive  generalizations.  Torrey, 
for  example,  devotes  some  ten  lectures  to  isolating,  weigh- 
ing, and  measuring  gases,  and  the  composition  and  syn- 
thesis of  water,  closing  the  series  by  a  lesson  on  the  internal 
structure  of  gases.  The  facts  brought  out  are  few,  but 
important.  Most  of  the  experiments  are  made  to  serve 
as  a  basis  for  inductive  reasoning,  though  the  author  very 
properly  uses  principles  well  known  to  chemists  to  com- 
plete the  explanation  of  what  to  the  student  would  be  but 
partially  understood,  as,  for  example,  the  citation  of 
Avogadro's  hypothesis  in  the  twentieth  lecture  to  general- 
ize the  facts  learned  concerning  the  internal  structure  of 
gases.1 

Some  chemical  works,  however,  are  entirely  devoid  of 
inductive  processes.  For  illustration,  Appleton's  "Short 
Course  in  Qualitative  Analysis"  devotes  itself  wholly  to  the 
establishment  of  tests,  first  for  the  metallic  elements,  in 
five  classes;  and  then  for  the  non-metallic  elements,  in  six 
classes.  The  student  is  first  informed  what  the  test  is, 
and  then  told  to  make  it.  Not  only  is  there  no  attempt  at 
1  Joseph  Torrey,  Jr.,  "Studies  in  Chemistry,"  Henry  Holt  &  Co.,  N.Y. 


THE    INDUCTIVE    APPROACH  1 07 

induction,  but  there  is  likewise  no  hint  given  as  to  how  this 
knowledge  is  to  be  applied.  There  may  be  justification 
for  such  courses,  especially  with  college  students  who  are 
beginning  a  professional  study  of  chemistry,  but  for  the 
high-school  student  certainly  those  works  that  stimulate 
him  to  use  his  mind  and  open  up  the  human  side  of  the 
science  are  greatly  to  be  preferred. 

Nowhere  are  the  initial  stages  of  an  inductive  study  of 
science  more  admirably  and  convincingly  set  forth  than  in 
Armstrong's  volume  on  "The  Teaching  of  Scientific 
Method."  *  Though  intended  for  teachers  of  elementary 
schools,  the  courses  and  methods  illustrated  are  of  equal 
interest  to  those  engaged  in  secondary  education. 

62.  There  is  ample  room  for  inductive  generalization 
both  in  biological  and  earth  sciences,  as  well  as  for  classi- 
fication and  the  determination  of  causes.  With  plants 
and  animals  we  may  make  inductive  studies  of  structure, 
of  the  function  of  organs  or  parts,  and  of  life  history.  In 
physical  geography  we  may  in  the  same  manner  approach 
the  laws  of  climate  as  determined  by  latitude,  elevation, 
the  prevalence  of  dry  or  moisture-laden  winds,  or  the 
action  of  storms  as  influenced  by  changes  in  temperature, 
in  barometric  pressure,  and  the  like.  In  brief,  there  is 
no  proposition  of  natural  science  which  may  not  be  ap- 
proached by  inductive  methods,  should  it  be  deemed 

1  Henry  E.  Armstrong,  "The  Teaching  of  Scientific  Method,"  The 
Macmillan  Co.,  N.Y. 


I08  SCIENTIFIC    METHOD    IN    INSTRUCTION 

desirable  to  do  so.  For  reasons  already  given,  however, 
and  for  others  still  to  be  discussed,  it  is  not  practicable 
to  conduct  all  instruction  even  in  the  natural  sciences  in 
this  manner. 

DISCUSSION  :  —  Illustrations  of  inductive  derivation  of 
generalizations  in  biology  and  in  the  earth  sciences. 

63.  As  is  well  known,  most  mathematical  reasoning  is 
deductive  in  character,  and  is  consequently  not  to  be 
treated  under  the  head  of  induction.  However,  as  has 
been  pointed  out  already  (Section  57),  there  is  a  species 
of  induction  which  is  not  only  legitimate,  but  highly  useful 
in  mathematical  teaching.  It  consists  in  prefacing  general 
demonstrations  by  particular  ones.  Thus,  in  leading  up 
to  the  general  formula  (a  +  by  equals  a2  +  2ab  +  ft2, 
the  student  may  be  called  upon  to  expand  such  expres- 
sions as  (2  +  3)2,  (3  +  4)2,  (4  4-  5)2,  and  then  to  perform  the 
operation  indicated  by  (a  +  6)2,  or  (a  +  b)  X  (a  +  &),  etc., 
until  the  formula  expresses  not  an  abstraction,  but  some- 
thing of  which  he  is  perfectly  cognizant.  In  the  same 
way,  before  relying  upon  a  general  demonstration  of  the 
binomial  theorem,  he  should  develop  by  actual  multipli- 
cation the  expressions  (a  +  &)2,  (a  +  ft)3,  (a  +  &)4,  (a  +  &)5, 
etc.  DeMorgan  says,  "We  believe  firmly,  that  to  the 
mass  of  young  students,  general  demonstrations  afford  no 
conviction  whatever;  and  that  the  same  may  be  said  of 
almost  every  species  of  mathematical  reasoning  when  it  is 
entirely  new."  Again,  "Inductive  reasoning  is  of  as  fre- 


THE    INDUCTIVE    APPROACH  IOQ 

quent  occurrence  in  the  sciences  as  any  other.  It  is 
certain  that  most  great  discoveries  have  been  made  by 
means  of  it;  and  the  mathematician  knows  that  one  of 
his  most  powerful  engines  of  demonstration  is  that  peculiar 
species  of  induction  which  proves  many  general  truths 
by  demonstrating  that,  if  the  theorem  be  true  in  one  case, 
it  is  true  for  the  succeeding  one.  But  the  beginner  is 
obliged  to  content  himself  with  a  less  rigorous  species  of 
proof,  though  equally  conclusive,  as  far  as  moral  certainty 
is  concerned.  Unable  to  grasp  the  generalizations  with 
which  the  more  advanced  student  is  familiar,  he  must 
satisfy  himself  of  the  truth  of  general  theorems  by  observ- 
ing a  number  of  particular  simple  instances  which  he  is 
able  to  comprehend."  l 

Nor  is  this  concrete,  inductive  approach  less  helpful 
in  geometry,  strict  deductive  science  as  it  is.  It  has  long 
been  the  custom  in  German  schools  to  precede  the  de- 
monstrative aspects  of  the  subject  by  a  long  series  of 
exercises  calculated  to  make  the  pupil  at  home  in  the 
terminology  and  conceptions  of  geometry,  by  familiar- 
izing him  with  forms  of  planes  and  solids,  and  with  con- 
crete constructions  and  experimental  proofs.  In  the 
United  States  this  kind  of  work  is  called  concrete  geom- 

1  Augustus  DeMorgan,  "  Study  and  Difficulties  of  Mathematics," 
pp.  183-184.  The  Open  Court  Publishing  Co.,  Chicago.  This  book 
cannot  be  too  highly  commended  to  the  young  teacher  and  student  of 
mathematics.  It  is  difficult  to  conceive  of  anything  more  lucid  and 
helpful. 


110  SCIENTIFIC    METHOD    IN    INSTRUCTION 

etry.  The  "Report  of  the  Committee  of  Ten"  upon  this 
subject  is  so  concise  and  convincing  that  the  greater  part 
of  it  is  here  inserted.  After  pointing  out  the  need  of  pre- 
liminary exercises  in  the  kindergarten  and  in  the  primary 
grades,  the  Report  continues  as  follows:  — 

"At  about  the  age  of  ten  for  the  average  child,  systematic 
instruction  in  concrete  or  experimental  geometry  should 
begin,  and  should  occupy  about  one  school  hour  per  week 
for  at  least  three  years.  During  this  period  the  main  facts 
of  plane  and  solid  geometry  should  be  taught,  not  as  an 
exercise  in  logical  deduction  and  exact  demonstration, 
but  in  as  concrete  and  objective  a  form  as  possible.  For 
example,  the  simple  properties  of  similar  plane  figures 
and  similar  solids  should  not  be  proved,  but  should  be 
illustrated  and  confirmed  by  cutting  up  and  rearranging 
drawings  or  models. 

"This  course  should  include  among  other  things  the 
careful  construction  of  plane  figures,  both  by  the  unaided 
eye  and  by  the  aid  of  ruler,  compasses,  and  protractor ; 
the  indirect  measurement  of  heights  and  distances  by  the 
aid  of  figures  carefully  drawn  to  scale;  and  elementary 
mensuration,  plane  and  solid. 

"The  child  should  learn  to  estimate  by  the  eye  and  to 
measure  with  some  degree  of  accuracy  the  lengths  of  lines, 
the  magnitudes  of  angles,  and  the  areas  of  simple  plane 
figures;  to  make  accurate  plans  and  maps  from  his  own 
actual  measurements  and  estimates,  and  to  make  models 


THE    INDUCTIVE    APPROACH  III 

of  simple  geometrical  solids  in  pasteboard  and  in 
clay. 

"Of  course,  while  no  attempt  should  be  made  to  build 
up  a  complete  logical  system  of  geometry,  the  child  should 
be  thoroughly  convinced  of  the  correctness  of  his  con- 
structions and  the  truth  of  his  propositions  by  abundant 
concrete  illustrations  and  by  frequent  experimental  tests; 
and  from  the  beginning  of  the  systematic  work  he  should 
be  encouraged  to  draw  easy  inferences,  and  to  follow  short 
chains  of  reasoning. 

"  From  the  outset  the  pupil  should  be  required  to  express 
himself  verbally  as  well  as  by  drawing  and  modelling,  and 
the  language  employed  should  be,  as  far  as  possible,  the 
language  of  the  science,  and  not  a  temporary  phraseology 
to  be  unlearned  later."  l 

Not  only  is  a  course  of  concrete  geometry  of  great  ser- 
vice to  the  demonstrative  aspects  of  the  subject,  but  an 
inductive  approach  to  the  more  difficult  propositions  is 
frequently  also  of  great  aid  to  the  demonstration  itself. 
An  instance  is  the  numerous  concrete  ways  of  prefacing 
the  demonstration  of  the  theorem  that  in  a  right  triangle 
the  square  on  the  hypothenuse  equals  the  sum  of  the 
squares  on  the  other  two  sides. 

DISCUSSION:  —  Illustrations  of  inductive  approach:  i.  in 
algebra;  2.  in  plane  geometry;  3.  in  solid  geometry. 

1  Report  of  the  Committee  of  Ten,  p.  no. 


112  SCIENTIFIC    METHOD    IN    INSTRUCTION 

64.  History  being  preeminently  the  realm  of  the  con- 
tingent,1 that  is,  of  a  class  of  causes  and  effects  which, 
unlike  those  revealed  by  natural  science,  do  not  follow  an 
invariable  order  of  natural  law,  but  are  influenced  and 
sometimes  determined  by  circumstances  that  might  have 
been  otherwise,  does  not  yield  itself  readily  to  general- 
ization as  a  form  of  explanation.  The  natural,  and 
indeed  almost  the  only  truly  historical,  form  of  explanation 
of  historical  events  is  that  of  cause  and  effect.2  Though 
one  writer  may  take  as  his  aim  "to  tell  how  it  actually 
was,"  the  complete  historian  must  add  "why  it  was" 
to  his  description  of  facts.  Otherwise,  though  we  had  the 
truth,  its  significance  would  be  left  to  surmise. 

There  are,  it  is  true,  certain  influences  arising  from 
historical  study  which  we  hope  to  bring  to  bear  upon  the 
character  of  the  student.  Enlightenment  as  to  the  rise 
and  development  of  civil  liberty  and  social  well-being 
should  clarify  the  judgment  of  youth,  develop  a  spirit  of 
toleration,  and  form  a  permanent  social  attitude  that 
shall  make  for  cooperative  good-will.  Yet,  if  we  try  to 
develop  from  history  generalizations  of  ethical  or  even 
pious  tenor,  we  shall  find,  in  any  attempt  to  be  specific, 
that  the  ethical  sword  is  two-edged,  and  cuts  both  ways. 
The  content  of  our  maxims  as  derived  from  specific 
examples  depends  upon  which  side  we  are.  People  still 

1  See  "  Principles  of  Secondary  Education,"  Vol.  I,  pp.  147-149. 
1  See  pp.  45-55. 


THE    INDUCTIVE    APPROACH  113 

dispute  as  to  whether  Charles  the  First  of  England  was  a 
martyr  who  died  an  unjust  death,  or  a  traitor  who  brought 
on  and  deserved  his  fate.  The  ethical  lessons  we  draw 
from  the  American  Revolution  might  change  their  value 
if  transported  to  England.  Whether  the  deeds  of  the 
French  Revolution  are  to  be  considered  a  just  return  for 
ages  of  abuse  of  the  people  by  the  nobles,  or  whether  it 
was  a  demonic  outbreak  incited  by  the  spirit  of  evil  and 
wreaking  its  blind  fury  upon  the  minority  who  alone 
upheld  civilization,  depends  upon  what  set  of  facts  re- 
ceives the  emphasis.  The  judicious  teacher  will  strive  to 
make  his  students  understand  the  whole  situation,  feeling 
sure  that  out  of  complete  understanding  will  grow  a  spirit 
of  toleration  toward  all  who  saw  only  in  part,  and  will 
leave  to  partisans  and  bigots  the  task  of  deriving  ethical 
generalizations  from  events  that  are  susceptible  of  giving 
rise  to  contradictory  principles  by  those  who  look  only 
at  the  other  side. 

DISCUSSION:  —  In  what  sense  and  to  what  extent  is  his- 
torical generalization  warrantable  ?  * 

65.  Custom  is  divided  between  the  inductive  and  the 
deductive  approach  to  the  study  of  a  foreign  language. 
The  older  procedure,  known  as  the  'translation'  method, 
relies  upon  the  memory  to  store  up  a  large  knowledge  of 
words,  inflections,  and  rules  of  syntax,  and  then  applies 

1  See  Publications  of  the  American  Economic  Association,  Third 
Series,  No.  2,  pp.  137-199. 

I 


114  SCIENTIFIC    METHOD    IN    INSTRUCTION 

these  deductively  in  translating  the  foreign  language  into 
the  vernacular.  The  avowed  final  purpose  of  the  older 
method  is  the  production  of  mental  discipline,  it  being 
assumed  that  a  student  who  can  master  a  subject  as  diffi- 
cult as  Latin  or  Greek  is  intellectually  capable  of  accom- 
plishing anything  not  impossible  to  the  mind.  This 
method  will  be  discussed  at  some  length  in  the  next  chapter. 
The  newer,  rival  method,  applied  especially  to  modern 
foreign  languages,  proceeds  by  inductive  approach  to  a 
mastery  of  words,  idioms,  inflections,  constructions,  and 
rules  of  syntax,  and  through  these  to  a  reading  and  speak- 
ing knowledge  of  the  language.  Pronunciation  is  taught 
by  a  system  of  comparative  phonetics,  in  which  the  sounds 
of  the  foreign  tongue  are  compared  to  those  of  the  ver- 
nacular, and  thoroughly  learned  by  constant  imitation 
and  practice.  This  new  method  was  forcibly  suggested  by 
Vietor  in  an  anonymous  essay  entitled,  "The  Teaching  of 
Languages  must  start  Afresh,"  and  in  which  the  main 
points  were  formulated  as  follows:1  "First',  foreign  lan- 
guages should,  primarily,  be  taught  by  means  of  con- 
nected types,  the  grammar  being  kept  in  the  background ; 
second,  imitation  and  thought  should  be  encouraged,  in- 
stead of  translation;  third,  pronunciation  should  be  taught 
upon  the  basis  of  scientific  phonetics;  and  fourth,  living 
languages  should  be  taught  before  dead  ones." 

'Russell,  "German  Higher  Schools,"  pp.  266-289.    No  teacher  of 
language  should  fail  to  read  these  illuminating  pages. 


THE    INDUCTIVE    APPROACH  115 

As  indicated  by  Russell :  "There  are  now  two  principal 
schools  of  language  teachers  in  Germany  diametrically 
opposed  in  doctrine.  The  representatives  of  the  old 
school  are  firmly  intrenched  in  the  Gymnasien  and  uni- 
versities, where  scholastic  ideas  largely  predominate, 
and  classical  training  with  a  view  to  mental  discipline 
receives  the  first  consideration.  The  reformers  count 
among  their  numbers  a  few  of  the  younger  university 
professors  and  Privat  Docenten  and  the  majority  of  in- 
structors in  the  Real  schools  and  Hohere  Tochterschu- 
len."  *  It  may  be  added  that  the  older  method  follows 
substantially  the  same  plan  in  both  ancient  and  modern 
foreign  languages,  since  their  aim  is  mental  discipline, 
rather  than  the  acquisition  of  literary  content  and  prac- 
tical mastery. 

Whatever  we  may  think  of  the  comparative  value  of  the 
two  methods  for  teaching  foreign  languages  to  adults  or 
to  youths  in  the  later  years  of  the  high  school,  the  inductive 
development  lesson  appears  to  have  almost  self-evident 
superiority  when  these  languages  are  begun  early ;  that  is, 
when  the  children  are  from  eight  to  twelve  or  fifteen  years 
of  age,  for  during  this  period  the  organs  of  speech  are 
plastic,  and  can  reproduce  any  sound  the  ear  is  capable  of 
perceiving,  while  interest  in  abstractions  and  their  de- 
ductive application  is  naturally  faint  and  can  be  enlisted 
only  by  pressure  or  by  a  high  quality  of  enthusiasm  and 

1  Russell,  "  German  Higher  Schools,"  p.  273. 


Il6  SCIENTIFIC    METHOD    IN    INSTRUCTION 

didactic  skill  on  the  part  of  the  teacher.  On  the  other 
hand,  the  concreteness,  vividness,  and  self-revealing  use- 
fulness of  cumulative  growth  in  the  comprehension  and 
practical  mastery  of  a  new  language,  such  as  is  possible 
when  the  inductive  method  is  skilfully  applied,  are  con- 
vincing evidences  that  this  method  in  the  hands  of  a  com- 
petent teacher  will  produce  the  best  results.  Certain 
elements  of  competency  for  the  successful  use  of  this 
method  must  be  presupposed.  They  are,  first,  ability 
to  speak  the  language  with  considerable  accuracy  and 
some  fluency;  and  second,  knowledge  of  comparative 
phonetics,  embracing  at  least  the  sounds  of  the  vernacular 
and  those  of  the  language  to  be  learned,  and  much  skill 
in  producing  them.  Given  these  two  qualifications,  all 
the  rest  is  but  an  application  of  customary  teaching  de- 
vices. Type  forms  will  be  presented,  drilled  upon,  com- 
mitted to  memory,  and  infinitely  varied;  grammatical 
forms  will  be  introduced  one  by  one,  dwelt  upon,  re- 
corded in  note-books,  and  constantly  repeated  until  use 
has  made  them  perfectly  familiar;  and  then  when  the 
pupils  can  read  with  some  facility,  the  text  will  be  read  by 
master  and  student,  the  meaning  analyzed  and  commented 
upon,  not  in  the  vernacular,  but  in  the  foreign  language. 
So  likewise  new  points  in  construction,  new  words,  new 
turns  of  expression,  will  be  noted  and  discussed,  still  in 
the  new  language.  Only  when  the  difficulty  cannot  be 
overcome  by  the  combined  knowledge  of  the  class,  is  the 


THE    INDUCTIVE    APPROACH  117 

vernacular  to  be  introduced  to  clear  it  up.1  Finally, 
selected  portions  containing  idiomatic  grammatical  or  other 
difficulties  may  be  translated  into  the  mother-tongue, 
but  no  translation  of  what  can  be  adequately  understood 
without  it  is  permitted.  The  thought  is  always  kept  in 
direct  touch  with  the  new  expression,  no  intermediary 
being  allowed.  As  courtship  is  always  most  engaging 
when  the  interested  parties  can  speak  face  to  face,  rather 
than  through  a  middleman,  say  the  father,  so  thought  and 
expression  get  on  best  together  when  they  are  not  divided 
by  an  interpreter,  even  if  that  interpreter  is  the  vernacular. 
Bearing  in  mind  that  the  schemer  is  always  superior 
to  his  scheme,  the  man  to  the  method,  it  may  be  said,  in 
general,  that  where  the  teacher  knows  the  language  he  is 
attempting  to  teach,  where  the  pupils  are  young,  and  the 
leading  objects  are  the  quickest  and  most  vital  apprehen- 
sion of  the  thought,  together  with  the  best  practical  com- 
mand of  the  new  tongue,  the  inductive  approach,  especially 
to  modern  foreign  languages,  is  greatly  to  be  preferred. 
On  the  other  hand,  where  the  teacher  has  only  a  reading 
knowledge  of  the  foreign  tongue,  where  the  students  are 
more  mature,  and  the  leading  objects  are  linguistic  disci- 
pline 2  and  the  rapid  acquisition  of  the  power  to  read,  then 
the  deductive  method  will  doubtless  be  most  effective. 

1  For  a  good  account  of  this  method  at  its  best,  see  Russell,  "  Ger- 
man Higher  Schools,"  pp.  266-290,  already  cited. 

1  See  "Principles  of  Secondary  Education,"  Vol.  I,  pp.  97-114- 


Il8  SCIENTIFIC    METHOD    IN    INSTRUCTION 

DISCUSSION:  —  i.  May  Latin  be  successfully  taught  with- 
out translation  ?  l  2.  Inductive  elements  in  the  Berlitz  system, 
the  Rosenthal  system,  etc.  3.  Compare  the  language  methods 
best  used  in  the  grades  with  those  most  effective  in  the  high 
school. 

66.  The  time-honored  method  of  teaching  English 
Grammar  in  England  and  the  United  States  is  deductive, 
in  that  the  student  learns  inflections,  definitions,  and  rules 
of  construction  as  given  by  authority  in  the  text-books,  and 
then  parses  and  construes  according  to  these  principles. 
In  Germany,  however,  where  but  little  use  is  made  of 
text-books,  the  student's  knowledge  of  grammar  is  built 
up  gradually  and  mostly  by  the  inductive  approach. 
The  first  is  economical  of  time  but  wasteful  of  under- 
standing; the  second  costs  time,  indeed,  but  is  rich  in 
insight  and  interest  and  develops  efficiency  in  use.  The 
inductive  approach  to  grammar,  much  more  than  the 
deductive,  leads  to  the  higher  language  sense,  whereby 
its  possessor  can  use  the  language  of  culture  with  as  much 
instinctive  ease  as  the  child  prattles  the  language  of  the 
home.2  Still,  education,  like  diplomacy  and  legislation, 
must  often  yield  some  desirable  things  in  order  to  get  others 
more  highly  esteemed.  The  best  teachers  here  as  else- 
where feel  free  to  use  the  book,  even  should  it  be  dogmatic 
and  thought-repressive,  because  of  its  condensed  and 

'See  Joseph  Payne's  description  of   Jacotot's  "Universal  Method" 
of  teaching  languages,  "Lectures  on  Education,"  pp.  341-386. 
1  See  "  Principles  of  Secondary  Education,"  Vol.  I,  p.  137. 


THE    INDUCTIVE    APPROACH  Up 

systematic  presentation,  but  at  the  same  time  leave 
scope  for  inductive  development  lessons  upon  points 
deemed  peculiarly  essential.  Matters  needing  only  clear 
statement  to  be  understood  may  well  be  presented  by 
abbreviated  methods,  but  when  subtle  distinctions  are  to 
be  apprehended,  as  in  the  classification  of  nouns  or  the 
modal  inflection  of  verbs,  time  is  actually  saved  by  the 
use  of  the  slower,  but  more  certain,  inductive  approach. 
An  additional  reason  why  the  high  school  may  limit  in- 
duction to  essentials  is  that  the  easier  conceptions  have 
already  been  acquired  by  inductive  processes  in  the  gram- 
mar school. 

DISCUSSION: — i.  Parts  that  (a)  parsing,  (6)  diagramming, 
(c)  sentence  analysis  should  play  in  the  teaching  of  high 
school  grammar.  2.  Place  and  function  of  comparative  and 
historical  grammar,  and  the  merits  of  induction  in  presenting 
them.1 

67.  Literature,  as  we  have  seen,  gives  rise  to  many 
problems,  all  of  which  may  be  investigated  by  inductive 
processes  through  a  study  of  the  works  themselves.  It  may 
be  well  to  suggest  with  Professor  Dowden  2  that  when  it 
comes  to  a  study  of  the  author  himself,  it  is  much  more 
profitable  to  examine  his  works  to  learn  what  manner  of 
man  he  is,  rather  than  to  consult  cyclopaedias  to  see  who 

1  See  Carpenter,  Baker  &  Scott,  "The  Teaching  of  English,"  pp.  202- 
219. 

3  Compare  Carpenter,  Baker  &  Scott,  "The  Teaching  of  English," 
PP-  255.  256. 


120  SCIENTIFIC    METHOD    IN     INSTRUCTION 

he  was,  when  he  lived  and  what  is  said  about  him.  Are 
his  senses  all  equally  keen  ?  Is  he  visual  minded  or  audi- 
tory minded  ?  Does  he  love  the  odors  of  flowers  and  field  ? 
Does  he  delight  in  the  touch  of  velvet?  Does  he,  like 
Browning  or  Kipling  or  Roosevelt,  revel  in  the  strenuous, 
in  the  swing  and  dash  of  vigorous  motion,  and  stirring 
deeds  ?  Or,  on  the  other  hand,  are  his  pleasures  found  in 
minor  aesthetic  thrills  that  arise  from  the  play  of  emotions 
so  subtle  as  to  escape  the  prosaic  mind  ?  What  emotions 
does  the  author  portray  most  effectively,  wonder  ?  terror  ? 
love?  grief?  hate?  revenge  (think  of  Portia,  Shylock, 
Othello,  Macbeth,  Rosalind,  etc.)?  What  feeling  has  he 
for  the  beautiful,  the  sublime,  the  humorous?  Is  he 
placid  or  fiery  (Carlyle,  Hugo)  in  his  temperament  ?  Are 
his  judgments  temperate  and  just  or  precipitate  and 
partisan?  Though  such  studies  as  these  are  made  in  the 
spirit  of  induction,  they  do  not  lead  to  generalizations, 
since  they  pertain  to  the  individual  alone ;  they  are  merely 
attempts  to  get  knowledge  at  first  hand,  and  hence  possess 
the  vital  character,  the  personal,  illuminating  vividness 
of  all  heuristic  investigations.  Not  only  does  the  search 
for  the  dominant  characteristics  of  an  author  as  manifested 
in  his  works  make  the  student  acquainted  with  his  literary 
personality  (the  only  one  that  concerns  the  reader),  but  it 
leads  also  to  deepening  literary  insight  and  appreciation. 

DISCUSSION:  —  Compare    physics,    biology,    mathematics, 
grammar,  and  literature  as  to  the  number  and  character  of  the 


THE    INDUCTIVE    APPROACH  121 

generalizations  that  may  profitably  be  derived  by  inductive 
processes. 

3.  Processes  of  Application  —  Induction 

(These  processes  are  essentially  deductive  in  character, 
and  will  be  treated  in  Chapter  VII.) 


CHAPTER  VI 
THE   DEDUCTIVE  APPROACH 

68.  The  general  purposes  of  the  deductive  approach 
are,  first,  to  enable  us  to  utilize  our  stored-up  experience 
in  order  to  anticipate  and  acquire  new  experience,  and 
second,  to  explain  facts  or  prove  new  propositions  on  the 
basis  of  causes,  classifications,  and  generalizations  already 
established.  The  word  because  (or  any  other  term  having 
the  same  meaning)  constitutes  its  formula.  For  illustra- 
tion, water  rises  in  the  pump,  because  it  is  forced  up  by 
the  outside  pressure  of  the  atmosphere  upon  the  surface 
of  the  water  outside  the  pump  when  the  pressure  on  the 
inside  is  lessened  by  the  act  of  pumping;  this  noun  must  be 
put  in  the  nominative  form,  because  it  is  the  subject  of  the 
verb;  these  triangles  are  equal,  because  two  sides  and  the 
included  angle  of  the  one  equal  two  sides  and  the  included 
angle  of  the  other;  population  tends  to  press  against  food 
supply,  because  the  one  increases  in  a  geometrical,  and  the 
other  only  in  an  arithmetical  ratio;  nitrogen  is  difficult 
to  fix,  because  it  has  such  slight  chemical  affinity  with  other 
elements,  and  when  fixed  makes  an  unstable  compound 
for  the  same  reason  (explosives  usually  contain  this 

element). 

taa 


THE    DEDUCTIVE    APPROACH  123 

Since  deduction  is  contrasted  to  induction  as  a  method 
of  acquiring  and  of  determining  the  meaning  of  facts, 
there  is  no  need  to  alter  the  formal  categories,  apper- 
ception, thought,  and  application. 

DISCUSSION  :  —  Contrast  between  the  methods  of  the  scho- 
lastic and  those  of  the  modern  man  of  science.  May  both  be 
justified  by  considering  the  nature  of  the  problems  each  tries 
to  solve  ? 

i.  Processes  of  Apperception  —  Deduction 

69.  As  already  briefly  explained  in  Section  5,  the  second 
stage  of  apperceptive  process  in  gaining  new  knowledge 
is  of  a  deductive  character,  in  that  we  use  our  stored-up 
experience  to  anticipate  what  to  look  for  and  what  we  may 
perhaps  expect  to  find.  This  is  true  in  all  acquisition  of 
knowledge  through  the  senses,  hence  in  direct  observation, 
whether  accompanied  by  experiment  or  not ;  *  and  it  finds 
a  manifold  use  in  the  schoolroom  in  the  form  of  what  may 
be  called  the  deductive  development  lesson  of  the  antici- 
patory type.  It  consists  hi  laying  the  foundation  for 
what  is  to  be  learned  through  forecasting  what  will  prob- 
ably be  found  true,  by  making,  on  the  basis  of  established 
principles,  a  series  of  tentative  deductions,  afterward 
to  be  tested  or  verified.  Thus  in  geography  the  climate 
of  any  region  may  be  inferred  from  the  conclusions  drawn 
from  the  known  influence  of  latitude,  elevation,  direction 

1  See  W.  T.  Harris,  "Psychologic  Foundations  of  Education,"  "Logic 
of  Sense  Perception,"  pp.  62-89. 


124  SCIENTIFIC    METHOD    IN    INSTRUCTION 

of  winds,  influence  of  ocean  or  mountains,  etc.1  In  like 
manner,  we  may  infer  what  the  industries  of  any  given 
section  of  the  country  will  be  when  we  know  what  the 
environment  of  the  people  is,  that  is,  what  sources  of  power 
and  of  raw  material  they  have,  what  the  quality  of  their 
soil  and  the  character  of  their  climate  are,  what  the  general 
status  of  their  civilization  is,  what  markets  they  enjoy, 
and  the  like.  Similarly  we  may  anticipate  what  the 
results  of  national  conflicts  will  be,  by  drawing  inferences 
from  our  understanding  of  the  conditions.  Men  usually 
forecast  also  the  probable  results  of  the  observations  and 
experiments  they  are  about  to  make,  for  "anticipation 
forward  points  the  view,"  not  only  in  the  larger  affairs 
of  life,  but  also  in  the  schoolroom.  No  one  should  be 
in  doubt  as  to  the  general  untrustworthiness  of  results  so 
obtained,  for  unforeseen  circumstances  are  likely  to  make 
the  inference  incorrect.  All  such  inferences  must,  of 
course,  be  rigidly  tested  by  resort  to  the  usual  means  for 
the  determination  of  hypotheses ;  namely,  observation,  and 
experiment ;  or  in  such  cases  as  arise  in  history  and  geog- 
raphy, the  authority  of  presumably  trustworthy  histori- 
ans or  geographers. 

The  usefulness  of  making  such  anticipatory  inferences 
lies  first  in  the  interest  aroused  by  the  effort  to  forecast 
results  by  applying  known  principles,  and  then  in  the 

'See  W.  C.  Bagley,  "The  Educative  Process,"  pp.  308-311,  for 
examples  of  such  anticipatory  use  of  deduction  in  the  elementary  school. 


THE    DEDUCTIVE    APPROACH 

direction  given  to  the  mind  by  the  effort.  Such  an  antici- 
pation is  a  form  of  hypothesis  suggested  by  previous 
experience,  and  can  be  used  to  advantage  by  the  teacher 
for  the  purposes  suggested;  namely,  the  stimulation  of 
interest  and  the  direction  of  attention.  Knowing  the 
unstable  condition  of  nitrogen  compounds,  the  experi- 
menter may  foresee  and  provide  for  possible  explosions; 
having  learned  that  aluminum  has  an  extraordinary 
affinity  for  oxygen,  the  teacher  may  inquire  what  the  action 
of  powdered  aluminum  would  be  when  mixed  with  oxide 
of  iron  under  the  influence  of  heat,  and  thus  anticipate 
the  surprising  effect  of  such  a  mixture  (called  thermite) 
when  chemical  action  is  set  up  by  the  explosion  of  a  little 
fulminate  of  mercury,  or  by  being  ignited  by  magnesium 
powder  set  off  by  a  bit  of  magnesium  ribbon.  A  few 
seconds  suffice  for  producing  molten  iron  of  a  very  high 
temperature,  the  oxide  of  iron  having  given  up  to  the 
powdered  aluminum  its  oxygen  and  developed  enough 
heat  in  the  chemical  action  to  produce  the  molten  iron.1 
"Coming  events  cast  then*  shadows  before:"  people 
busy  themselves  with  forecasting  the  probable  results  of 
coming  elections,  the  effects  of  new  inventions,  the  con- 
sequences that  may  be  expected  to  follow  the  establish- 
ment of  new  industries,  or  the  promulgation  of  new 

1  The  gray  appearance  of  the  metal  is  due  to  a  covering  r  "  rust  which 
forms  instantly  upon  its  exposure  to  the  oxygen  of  the  air,  but  it  is  so 
dense  that  it  protects  the  aluminum  from  further  oxydation.  Thus  in 
this  case  rust  is  a  protection  against  rusting. 


126  SCIENTIFIC    METHOD    IN    INSTRUCTION 

policies,  or  the  transformation  to  be  brought  about  by 
new  economic  conditions.  Examples  are  seen  in  pres- 
idential elections,  the  invention  of  the  telegraphone, 
wireless  telegraphy,  the  internal-combustion  engine,  the 
steam  turbine,  cotton-mills  in  the  South,  the  destruction 
of  the  forests  and  the  exhaustion  of  the  coal  supply,  the 
effects  of  the  Southern  labor  problem  upon  the  prohibition 
of  the  liquor  traffic,  as  well  as  the  effect  upon  total  absti- 
nence of  the  decision  of  great  railroad  companies  to  lay 
off  first  those  who  are  addicted  to  the  liquor  habit,  when 
reductions  of  the  force  are  needed.  The  academic  world 
recently  surmised  what  the  authorities  of  Swarthmore 
College  would  do,  when  offered  a  large  bequest  on  condition 
of  permanently  abolishing  all  intercollegiate  athletics. 
Some  predictions  were  based  upon  hopes  and  prejudices, 
according  as  such  athletics  were  favored  or  opposed,  and 
some  were  based  on  more  fundamental  considerations, 
such  as  the  moral  right  of  one  Board  of  Managers  to 
decide  for  all  time  the  policy  of  the  college  upon  important 
matters.  The  bequest  was  finally  declined  on  the  ground 
that  the  Board  of  Managers  had  no  such  moral  right. 

A  method  of  thought  of  such  universal  use  in  the  outside 
world  is  worthy  of  careful  consideration  in  the  teaching 
of  youth.  Patrick  Henry  exclaims,  "  I  know  of  no  way  of 
judging  >f  the  future  but  by  the  past."  Not  a  very  re- 
liable way,  it  may  be  urged,  but  such  as  it  is  it  constitutes 
our  chief  means  of  utilizing  history  to  forecast  events, 


THE    DEDUCTIVE    APPROACH  127 

to  warn  of  dangers,  and  to  reveal  opportunities.  Con- 
sequently some  preliminary  training  in  anticipating  the 
probable  effects  of  a  given  set  of  historical  conditions  may 
well  be  a  part  of  a  good  historical  method.  This  can  easily 
be  applied  in  any  situation  through  varying  an  actual 
condition  by  substituting  another  that  might  have  taken 
its  place.  Thus,  for  example,  what  would  have  been  the 
result  if  Louis  XVI  of  France  had  granted  a  constitution 
and  a  real  representative  government  to  the  people  before 
the  outbreak  of  the  Revolution  ?  if  Charles  I  of  England 
had  met  the  situation  in  that  country  in  a  spirit  of  strict 
honesty  and  conciliation  ?  if  the  United  States  government 
had  offered  to  pay  a  just  price  for  the  liberation  of  every 
slave  in  the  South,  say  in  1860  ?  Or,  looking  to  the  future, 
what  would  now  be  the  effect  upon  Russia  if  the  Czar  and 
the  bureaucracy  should  abrogate  enough  arbitrary  power 
to  give  that  country  a  real  representative  government? 
In  historical  study,  where  the  student  has  not  instant  access 
to  the  facts,  but  must  search  for  them  at  some  length,1 
similar  forecastings  as  to  probable  outcome  are  in  order. 
Literature  offers  a  good  field  for  the  exercise  of  the 
anticipatory  judgment,  since  it  is  supposed  to  represent 
events  and  results,  not  so  much  as  they  are  or  were,  but 
as  they  might  have  been  or  ought  to  be.  In  such  matters, 
the  student  may  well  have  a  chance  to  try  his  ingenuity 

1  See  Joseph  E.  Chamberlain,  "  Ifs  of  History,"  Henry  Altemus  Co., 
Philadelphia,  1908. 


128  SCIENTIFIC    METHOD    IN    INSTRUCTION 

and  his  ethical  insight.  Any  literary  work  offers  opportu- 
nities for  such  experiments,  either  by  supposing  a  change 
in  some  essential  part,  or  by  varying  the  time  and  the  place 
which  furnish  the  setting  for  the  piece,  or,  even  without 
any  such  change,  by  supposing  a  different  result  to  follow 
from  the  given  combination  of  circumstances.  What,  for 
example,  would  have  been  the  effect  on  the  outcome  of 
the  "Merchant  of  Venice  "  had  Shylock  yielded  to  Portia's 
plea  for  mercy  and  had  bid  her  destroy  the  bond  ?  What, 
if  the  judge  had  condemned  him  to  death  ?  What,  if  the 
Prince  of  Morocco  had  chosen  the  right  casket?  Could 
Portia  have  extricated  herself  from  her  painful  position 
as  skilfully  as  she  did  Antonio  from  his?  Can  you 
suggest  a  better  plan  for  Bassanio  to  get  rid  of  his  debts 
than  to  marry  a  rich  wife?  What  would  the  modern 
woman  have  said  when  Bassanio  chose  the  leaden  casket  ? 
In  short,  in  literary  study  the  student  should  not  be  denied 
the  use  of  that  power  which  Hamlet  exercised  when  he 
exclaimed,  "Oh  my  prophetic  soul,  my  Uncle  ! " 

Having  hit  upon  his  grand  generalization,  namely, 
natural  selection  under  the  influence  of  the  struggle  for 
existence,  the  mind  of  Darwin  leaped  forward  to  a  thou- 
sand surmises,  anticipations  of  what  he  would  find  when 
the  principle  was  applied,  now  in  this,  now  in  that  direc- 
tion, so  that  from  this  one  grand  apperceptive  basis,  he 
was  able  to  formulate  a  host  of  hypotheses  concerning 
kindred  phenomena.  These  hypotheses  or  anticipations 


THE    DEDUCTIVE    APPROACH  1 29 

he  was  able  at  leisure  to  verify  or  show  to  be  inadequate 
as  the  case  might  be.  The  road  to  similar  exercises  of 
this  power  on  the  part  of  the  student  has  not  yet  been 
closed  in  the  biological  and  other  sciences.  The  applica- 
tion of  tests  to  discover  the  elements  of  a  chemical  com- 
pound, so  far  as  they  are  not  controlled  by  a  fixed  routine, 
are  of  the  nature  of  hypothetical  anticipations. 

DISCUSSION  :  —  Illustrations  of  suitable  opportunities  for 
the  use  of  anticipatory  judgments  on  the  part  of  students  in 
(i)  the  various  sciences,  physics,  chemistry,  zoology,  botany, 
physical  geography;  (2)  literature;  (3)  history;  (4)  econom- 
ics; (5)  artistic  representation. 

2.  Processes  of  Thought  —  Deduction 

70.  The  function  of  deduction  proper  is  the  explana- 
tion of  facts  or  the  proof  of  new  propositions  on  the  basis 
of  causes,  classifications,  and  generalizations  already 
established.  These  may  appear  in  the  guise  of  axioms  of 
thought;  laws  of  cause  and  effect;  of  logical  necessities; 
principles  of  grammar  or  ethics;  theories  and  laws  of 
mind,  of  physical  and  biological  science  and  of  human 
institutions,  and  the  like.  A  teacher  who  thinks  only  of 
teaching  a  subject  is  as  prone  to  deduction  as  the  sparks 
to  fly  upward.  The  reason  is  not  far  to  seek.  So  far  as 
his  class  is  concerned,  the  subject  is  a  completed  science. 
Its  facts  are  well  known,  its  generalizations  well  estab- 
lished and  practically  unquestioned.  Why  use  indirec- 


130  SCIENTIFIC    METHOD    IN    INSTRUCTION 

tion  to  find  direction  out  ?  Why  not  impart  the  facts  and 
laws  quickly  by  authority,  thus  saving  time  and  labor  for 
all  concerned?  It  is  only  when  the  chief  function  of 
teaching  is  seen  to  be  to  teach  the  subject  to  the  student, 
that  the  universal  validity  of  the  deductive  procedure  is 
questioned.  Nevertheless,  life  is  short  and  art  is  long; 
furthermore,  the  student  himself  gradually  acquires  a 
knowledge  of  general  principles  which  it  were  sheer  waste 
not  to  use  in  the  acquisition  of  new  facts  and  insights. 
Just  as  every  thinker  utilizes  his  grasp  of  general  prin- 
ciples to  solve  minor  problems,  so  the  student  should 
likewise  form  the  habit  of  relying  on  the  basal  principles 
of  grammar,  physics,  chemistry,  biology,  economics,  or 
ethics,  which  he  has  acquired,  to  clear  up  subordinate 
points  that  need  explanation.  The  laws  of  mechanics 
will  enable  him  to  understand  any  machine ;  the  principle 
of  cross-fertilization  makes  clear  the  production  of  new 
and  better  varieties  by  plant  breeding;  the  laws  of  gram- 
mar enable  him  to  explain  any  given  construction  in  litera- 
ture ;  a  comprehension  of  mathematical  axioms  renders  a 
geometrical  proof  easy  to  understand  and  possible  to  con- 
struct, and  so  on  throughout  the  whole  domain  of  knowl- 
edge. In  this  connection  it  should  be  noted  that  nearly 
all  the  explanations  that  intelligent  adults  give  to  children 
rest  upon  this  deductive  movement.  "Why,"  asks  the 
lad,  "do  the  flame  and  smoke  go  up  the  flue  of  the 
chimney?"  "Because,"  replies  the  adult,  in  substance, 


THE    DEDUCTIVE    APPROACH  131 

"air  that  is  heated  expands  and,  occupying  more  space, 
becomes  lighter  than  the  same  volume  of  air  by  which  it 
is  surrounded.  But  the  atmosphere  being  heavy  enough 
to  press  down  everywhere  with  a  weight  of  many  pounds 
per  square  inch  naturally  presses  the  volume  of  ah*  made 
lighter  by  heat  up  the  chimney."  "If  the  rivers  all  run 
into  the  ocean,  why  does  not  the  ocean  overflow?" 
Then  follows  a  description  of  evaporation,  the  formation 
and  movement  of  clouds,  the  falling  of  rain,  snow,  etc. ;  in 
short,  the  forms  and  circulation  of  water  are  explained. 
In  like  manner  adults  explain  to  children  all  the  simple 
phenomena  by  which  they  are  surrounded  —  the  boulders 
in  the  field;  the  ice  on  the  pond;  the  heating,  ventilating, 
and  plumbing  systems  in  the  houses;  the  machines  that 
are  run  by  steam,  gas,  or  electricity;  why  matches  light; 
why  gunpowder  and  dynamite  explode;  why  boats  float, 
etc.  Were  one  asked,  What,  from  the  deductive  stand- 
point, is  the  difference  between  nature  study  in  the  grades 
and  natural  science  in  the  high  school  ?  the  reply  would  be, 
In  nature  study  we  utilize  generalizations  well  known  to 
the  teacher  to  explain  the  given  phenomena,  quite  after 
the  manner  of  home  explanations ;  whereas  in  high-school 
science  we  try  to  establish  and  verify  the  laws  themselves. 
In  the  first  case  established  laws  are  used  to  explain  the 
facts;  in  the  second  the  facts  are  used  to  lead  up  to  and 
verify  the  laws.  The  student  should  not  jump  to  the  con- 
clusion, however,  that  nature  study  consists  wholly  in  ex- 


132  SCIENTIFIC    METHOD    IN    INSTRUCTION 

planations  of  the  kind  above  described,  for  it  has  also  an 
important  experimental,  observational,  and  inductive  basis. 

DISCUSSION  :  —  Extent  to  which  the  nature-study  method 
is  desirable  in  the  teaching  of  science  in  the  high  school. 

71.  When  its  legitimate  limit  is  passed,  every  method  of 
teaching  has  its  dangers  and  evils.  The  most  imminent 
danger  in  the  excessive  use  of  the  deductive  method  is 
that  initiative,  originality,  and  native  thinking  power, 
and  the  consequent  intentness  and  alertness  of  mind  that 
go  with  them,  will  become  atrophied  for  lack  of  exercise, 
and  that  authority  will  be  accepted  for  truth  in  the  realm 
of  fact,  while  formalism  will  take  the  place  of  spontaneity 
in  reasoning.  When  such  is  the  case  thought  is  robbed  of 
its  vitality,  and  becomes  not  unlike  that  ascribed  by  a 
Swarthmore  College  student  to  the  skeleton  that  hangs 
in  a  glass  case  in  the  biological  museum:  — 

"  I  think  and  I  think, 
But  I  get  nothing  thunk." 

To  keep  alive  the  native  intellectual  powers  under  the 
deductive  method,  the  teacher  of  the  natural  sciences 
relies  upon  the  adequate  verification  of  the  laws  given  at 
first  upon  the  authority  of  the  book  or  of  himself.  There 
is  here  scope  for  the  scientific  stages  of  observation  and 
experiment  and  some  room  also  for  the  drawing  of  new 
inferences.  Here  again,  however,  scientific  men  utter  a 
word  of  caution,  for  the  student,  knowing  what  he  is  ex- 
pected to  prove,  becomes  greatly  biassed  in  his  observations 


THE    DEDUCTIVE    APPROACH  133 

and  inferences.    Furthermore,  if  he  trusts  the  authority 
that  gave  him  his  principle,  he  is  likely  to  exclaim,  "What's 
the  use  of  trying  to  verify  a  proposition  of  which  I  am 
already  absolutely  sure?"    His  work  becomes  perfunc- 
tory, and  observations  are  interpreted  not  for  what  they 
actually  reveal,  but  according  to  the  results  expected. 
Thus  the  scientific  spirit  is  paralyzed  in  the  house  of  its 
friends.1    The  same  effect  is  produced,  of  course,  when  a 
student  is  asked  to  demonstrate  by  long  inductive  process 
that  a  given  principle  of  the  text-book  is  true.    If,  how- 
ever, the  student  is  hi  some  doubt  as  to  what  the  end  of 
his  induction  is  to  be,  or  tries  his  verification  to  see  if  a 
given  principle  will  hold  when  applied  in  a  new  way,  then 
the  effort  seems  worth  while,  and  the  student  is  likely  to 
work  with  interest  and  ardor,  rather  than  with  passive 
indifference.    Upon  one  thing  all  thinkers  seem  resolved, 
no  matter  in  what  domain  of  thought  they  may  work,  and 
that  is,  that  the  intellectual  world  shall  never  again  settle 
into  the  dogmatic  complacency  that  characterized  it  dur- 
ing the  scholastic  age,  when  men  forgot  to  ask  whether 
the  premises  from  which  they  reasoned  were  true  and  ade- 
quate, or  whether  anything  new  might  be  learned  by  first- 
hand observation  and  experiment  concerning  the  men  and 
things  about  them.    The  same  resolution  should  animate 
the  school.    Dogmatic  complacency  is  a  deplorable  state 

1  Compare  Edwin  H.  Hall  (Smith  &  Hall),  "The  Teaching  of  Chem- 
istry and  Physics,"  pp.  274-288.     Longmans,  Green  &  Co.,  N.Y. 


134  SCIENTIFIC    METHOD    IN    INSTRUCTION 

for  even  adults  to  be  in;  for  youth  it  is  intolerable.  Youth 
is  naturally  buoyant,  hopeful,  curious,  daring,  inventive, 
inquiring ;  and  every  true  teacher  will  desire  to  stimulate, 
develop,  and  guide  these  tendencies  to  fruitful  ends,  not 
to  hypnotize  them  into  quiescence  by  the  baleful  eye  of 
authority. 

Notwithstanding  their  shortcomings  as  a  universal 
method,  deductive  processes  have  ever  been  and  perhaps 
will  ever  be  the  main  reliance  of  the  schoolmaster  in  the 
training  of  youth.  The  greatest  educational  triumphs  of 
the  past  have  been  achieved  by  the  aid  of  this  method, 
for  it  is  almost  the  inevitable  way  in  which  demonstra- 
tive mathematics  must  be  studied,  and  it  has  been  the 
favorite,  and  in  essential  respects  the  necessary,  method 
of  linguistic  training. 

DISCUSSION  :  —  i.  Means  of  preventing  a  mere  perfunctory 
use  of  observation,  experiment,  and  verification  in  the  natural 
sciences.  2.  Means  of  preventing  growth  of  dogmatic  com- 
placency arising  from  undue  reliance  upon  authority  as  the 
basis  of  explanation  and  argument. 

72.  It  is  always  declared,  but  not  always  convincingly 
shown,  that  mathematics,  especially  geometry,  is  a 
deductive  science.  To  convince  the  student  that  this  is 
true,  and  that  deductive  methods  must  sooner  or  later 
be  used  in  order  to  get  the  legitimate  results  of  mathe- 
matical training,  the  following  citations  from  DeMorgan 
are  made.1  After  contrasting  the  probable  character 

1  "The  Study  and  Difficulties  of  Mathematics,"  pp.  4-10. 


THE    DEDUCTIVE    APPROACH  135 

of  historical  evidence  with  the  convincing  certainty  of 
that  of  mathematics,  he  continues  as  follows:  "We  have 
said  that  the  nature  of  mathematical  demonstration  is 
totally  different  from  all  other,  and  the  difference  con- 
sists in  this  —  that  instead  of  showing  the  contrary  of  a 
proposition  asserted  to  be  only  improbable,  it  proves  it  at 
once  to  be  absurd  and  impossible.  This  is  done  by  show- 
ing that  the  contrary  of  a  proposition  which  is  asserted  is 
in  direct  contradiction  to  some  extremely  evident  fact  of 
the  truth  of  which  our  eyes  and  hands  convince  us.  In 
geometry,  of  the  principles  alluded  to,  those  which  are 
most  commonly  used  are :  — 

"i.  If  a  magnitude  be  divided  into  parts,  the  whole  is 
greater  than  either  of  those  parts. 

"2.  Two  straight  lines  cannot  inclose  a  space. 

"3.  Through  one  point  only  one  straight  line  can  be 
drawn,  which  never  meets  another  straight  line,  or  which 
is  parallel  to  it. 

"It  is  on  such  principles  as  these  that  the  whole  of  geom- 
etry is  founded,  and  the  demonstration  of  every  proposi- 
tion consists  hi  proving  the  contrary  of  it  to  be  inconsis- 
tent with  one  of  these. 

"But,  although  there  is  no  other  study  which  presents 
so  simple  a  beginning  as  that  of  geometry,  there  is  none  in 
which  the  difficulties  grow  more  rapidly  as  we  proceed, 
and  what  may  appear  at  first  as  rather  paradoxical,  the 
more  acute  the  student  the  more  serious  will  the  impedi- 


136  SCIENTIFIC    METHOD    IN    INSTRUCTION 

ments  in  the  way  of  his  progress  appear.  This  necessa- 
rily follows  in  a  science  which  consists  of  reasoning  from 
the  very  commencement,  for  it  is  evident  that  every  student 
will  feel  a  claim  to  have  his  objections  answered,  not  by 
authority,  but  by  argument,  and  that  the  intelligent  stu- 
dent will  perceive  more  readily  than  another  the  force  of 
an  objection  and  the  obscurity  arising  from  an  unex- 
plained difficulty,  as  the  greater  is  the  ordinary  light  the 
more  will  occasional  darkness  be  felt. 

"  Mathematics  are  peculiarly  well  adapted  for  this  pur- 
pose (training  the  powers  of  deductive  reasoning),  on  the 
following  grounds :  — 

"i.  Every  term  is  distinctly  explained,  and  has  but 
one  meaning,  and  it  is  rarely  that  two  words  are  employed 
to  mean  the  same  thing. 

"2.  The  first  principles  are  self-evident,  and,  though 
derived  from  observation,  do  not  require  more  of  it  than 
has  been  made  by  children  in  general. 

"3.  The  demonstration  is  strictly  logical,  taking  noth- 
ing for  granted  except  the  self-evident  first  principles, 
resting  nothing  upon  probabilities,  and  entirely  indepen- 
dent of  authority  and  opinion. 

"4.  When  the  conclusion  is  attained  by  reasoning,  its 
truth  or  falsehood  can  be  ascertained,  in  geometry  by 
actual  measurement,  in  algebra  by  common  arithmetical 
calculation. 

"5.  There  are  no  words  whose  meanings  are  so  much 


THE    DEDUCTIVE    APPROACH  137 

alike  that  the  ideas  which  they  stand  for  may  be  con- 
founded. Between  the  meanings  of  terms  there  is  no 
distinction,  except  a  total  distinction,  and  all  adjectives 
and  adverbs  expressing  difference  of  degrees  are  avoided." 
From  the  foregoing  remarks  it  may  easily  be  seen  that 
geometry  begins  with  axioms  for  the  basis  of  its  arguments, 
and  that  as  the  subject  unfolds,  propositions  once  estab- 
lished on  the  basis  of  axioms  become  in  turn  the  premises 
from  which  further  deductions  are  made,  and  so  on 
through  all  the  geometrical  propositions  undertaken  by 
the  student,  who  has  ever  the  consciousness  that  if  the 
validity  of  any  previous  proposition  he  uses  is  questioned, 
it  may  be  led  back  directly  to  those  fundamental  percep- 
tions of  truth  with  which  he  started.  In  algebra,  the 
reasoning  has  the  same  axiomatic  basis,  for  in  an  equation 
where  one  side  is  numerically  equal  to  the  other,  any 
operation  may  be  performed  which  does  not  contradict 
any  of  these  axioms,  which  usually  pertain  to  additions  to. 
subtractions  from,  or  multiplication  or  division  of,  equals. 
Besides,  as  DeMorgan  says,  the  results  may  be  tested  by 
arithmetical  computations.  As  was  explained  in  Section 
62,  the  only  inductive  approach  possible  hi  mathematics 
is  that  which  consists  hi  anticipating  general  demonstra- 
tions by  specific  ones.  This  is  legitimate  and  highly  use- 
ful as  an  introduction,  but  hi  the  end  a  student  either 
comprehends  a  deductive  demonstration,  or  he  has  not 
touched  the  heart  of  mathematics. 


138  SCIENTIFIC    METHOD    IN    INSTRUCTION 

DISCUSSION  :  —  Means  of  introducing  students  to  a  clear 
conception  of  what  is  and  what  is  not  a  demonstration. 

73.  Teachers  should  not  delude  themselves  with  the 
notion  that  when  they  have  asked  a  student  to  read  and 
reproduce  a  demonstration  in  geometry  they  have  really 
given  him  exercise  in  deductive  thinking,  for  the  simple 
fact  is,  that  the  thought  is  the  author's,  not  the  student's. 
One  procedure  of  this  nature  is  to  require  the  student 
thus  to  read  and  reproduce  all  the  demonstrations  given 
in  the  book.  If  he  have  a  good  memory  and  is  able  to 
perceive  the  force  of  the  argument,  he  may  undoubtedly 
gain  a  good  deal  of  geometrical  knowledge  and  insight. 
The  opposite  plan,  and  the  one  usually  followed  in  German 
schools,  is  to  place  no  completed  demonstrations  whatever 
before  the  student,  but  to  assign  the  proposition,  ask  a 
few  questions  about  it  to  set  him  on  the  right  track,  and 
require  him  to  work  it  out  for  himself.  A  third  plan  com- 
bines the  first  two,  in  that  a  certain  number  of  funda- 
mental theorems  are  given  in  full  by  the  author,  read  and 
reproduced  by  the  student,  who  then  proceeds  to  do  some 
geometrizing  on  his  own  account  by  solving  a  number  of 
'originals'  containing  variations  of  the  type  proposition. 
Judiciously  used,  this  plan  is  in  general  by  far  the  best  of 
the  three  mentioned,  for  it  gives  scope  for  real  work  on 
the  part  of  the  student  while  at  the  same  time  keeping  him 
in  close  touch  with  demonstrations  of  unquestioned  valid- 
ity. It  takes  a  teacher  unusually  well  versed  in  geomet- 


THE    DEDUCTIVE    APPROACH  139 

rical  reasoning  to  pursue  the  second  plan  with  the  best 
results,  for  unless  the  student's  thought  is  held  rigidly  to 
real  demonstration,  much  loose  thinking  and  many  bad 
habits  of  thought  are  engendered.  Where  a  dozen  forms 
of  proof  are  handed  in  at  one  time,  only  the  expert  geome- 
trician can  at  once  say  what  is  logically  correct  and  what 
fallacious. 

In  assisting  students  to  do  real  thinking  in  geometry, 
a  number  of  the  aspects  of  the  problem  should  be  held 
constantly  before  the  mind,  especially  the  following:  — 

1.  What  is  given  and  what  to  prove  in  this  proposition? 

2.  How  construct  a  figure  that  will  give  a  clew  to  the 
solution  ? 

3.  What  equalities  (or  inequalities)  must  be  proved  in 
order  to  demonstrate  the  proposition  ? 

4.  How  can  we  use  our  axioms  or  previous  propositions 
to  prove  these  equalities  (or  inequalities)? 

For  illustration,  take  a  very  simple  proposition:  — 
In  any  triangle,  any  exterior  angle  equals  the  sum  of  the 
two  interior  non-adjacent  angles. 

1.  Given  the  triangle  ABC,  with  side  AB  produced  to 
X  to  show  an  exterior 

angle,   the   proposition 
being  that  angle  CBX 

equals  the  sum  of  an- 

A  B 

gles  a  and  c. 

2.  How  construct  a  figure  that  will  give  a  clew  to  the 


140  SCIENTIFIC    METHOD    IN    INSTRUCTION 

solution?  It  will  quickly  occur  to  some  student  that 
since  the  exterior  angle  is  equal  to  two  others  (a  and  c] 
it  may  be  possible  to  divide  it  into  two  parts,  one  of 
which  shall  be  equal  to  a,  and  the  other  to  c.  How  can 
this  be  done  ?  Think  of  a  previous  construction  in  which 
c  would  be  equal  to  a  certain  other  angle.  How  then  shall 
we  draw  the  new  line  that  is  to  divide  the  exterior  angle  ? 
Parallel  to  AC. 

3.  What  equalities  appear?    Angle  x  is  equal  to  angle 
c,  because  (4)  alternate  angles  formed  by  a  transversal 
with    two    parallels    are    equal    (previous    proposition). 
What  other  angles  must  be  equal,  if  the  proposition  is 
true?    Angle  y  must  be  equal  to  angle  a.    Is  it?    Yes, 
(4)  because  a  line  cutting  two  parallels  makes  correspond- 
ing angles  equal  (previous  proposition). 

4.  What  follows?    That  angle  CBX  equals   the  sum 
of  the  two  interior  non-adjacent  angles  (axiom). 

DISCUSSION: —  i.  Comparison  of  text-books  for  variations 
of  these  three  fundamental  plans  in  deductive  geometry.  2. 
Methods  of  stimulating  the  student's  invention  in  construction.1 

74.  Linguistic,  like  mathematical  training,  has  long 
been  a  gymnasium  for  the  exercise  of  deductive  reason. 
The  concepticns,  rules,  and  principles  of  grammar,  also 

1  Consult  Elisha  S.  Loomis,  "Original  Investigation,  or  How  to 
Attack  an  Exercise  in  Geometry,"  pp.  1-23,  Ginn  &  Co.;  consult  also 
Wm.  W.  Rupert,  "Famous  Geometrical  Theorems  and  Problems,  with 
their  History,"  D.  C.  Heath  &  Co. 


THE    DEDUCTIVE    APPROACH  141 

of  rhetoric  and  argumentation  or  dialectics,  are  first  com- 
prehended and  learned,  and  then  deductively  applied  in 
translation  and  composition  in  order  to  make  out  or  ex- 
press meaning.1  Even  if  the  principles  of  grammar  were 
all  inductively  derived  in  the  first  place,  they  would  have 
to  be  used  deductively  in  translation,  since  meaning 
depends  on  construction,  and  this  in  foreign  languages  is 
usually  determined  by  grammatic  form:  Puer  puellam 
amat,  or  Puellam  puer  amat,  or  Amat  puer  puellam,  etc. 
The  order  is  much  less  elastic  in  English  where  inflectional 
forms  have  disappeared  and  the  grammatical  construction 
of  a  word  can  be  determined  only  by  the  meaning  of  the 
sentence.  Here  the  process  is  still  deductive,  as  when  we 
say,  this  noun  is  hi  the  objective  case,  because  it  names 
the  receiver  of  an  action,  instead  of  the  usual  opposite 
statement,  —  this  noun  names  the  receiver  of  an  action, 
because  it  has  the  form  of  the  accusative.  The  fact  that 
English  is  now  so  little  modified  by  inflection  has  led  not 
a  few  authors  and  more  teachers  to  present  grammar,  not 
so  much  for  the  aid  it  gives  in  comprehension  and  compo- 
sition, as  an  end  in  itself.  The  subject  is  taught  until  its 
distinctions  are  understood,  and  then  having  been '  learned ' 
is  dropped.  It  can  hardly  be  asserted  that  such  a  pro- 
cedure is  valueless,  but  it  may  be  confidently  asserted  that 
it  is  comparatively  so.  The  chief  disciplinary  effect  re- 

1  Compare  Vol.  I  of  this  work,  "Function  and  Worth  of  Linguistics," 
pp.  97-119. 


142  SCIENTIFIC    METHOD    IN    INSTRUCTION 

suiting  from  the  teaching  of  foreign  languages  arises,  not 
so  much  from  the  fact  that  a  few  distinctions  have  been 
comprehended,  as  that  they  have  been  deductively  used  in 
translation  of  thousands  of  pages  of  classic  writings.1  It 
is  in  this  way  that  there  is  effected  the  introspective  train- 
ing of  the  mind,  first  to  perceive  and  then  to  express  all 
the  shades  of  meaning  language  can  embody.  The  mod- 
ern youth's  grandfathers  had  a  better  linguistic  training  in 
English  than  he  now  enjoys,  for  whereas  the  youth  applies 
his  morsel  of  grammar  to  scraps  of  literature,  the  grand- 
father parsed  Milton's  "Paradise  Lost"  and  Pope's 
"Essay  on  Man,"  entire.  The  one  takes  his  grammar 
like  a  pill,  to  be  swallowed  and  thus  made  an  end  of;  the 
other  used  his  as  a  means  of  unlocking  the  intellectual 
treasures  of  grand  systems  of  thought.  Both  plans  use 
the  deductive  movement,  the  one  effectively  and  the 
other  ineffectively.  It  is  not  to  be  inferred  that  we  must 
do  just  as  our  grandfathers  did,  but  only  that  whenever 
means  are  transformed  into  ends,  such  ends  are  hardly 
worth  striving  for. 

In  translation,  every  sentence  becomes  a  problem,  and  if 
it  chances  to  be  a  difficult  one,  many  are  the  hypotheses 
that  must  be  proposed,  examined,  and  rejected  before  the 
right  ones  are  hit  upon  and  the  meaning  revealed.  The 
form  of  a  word  suggests  a  given  construction.  An  hypoth- 
esis may  be  instantly  formed  on  this  basis,  only  perhaps 

1  See  discussion  in  Vol.  I  of  this  work,  pp.  111-114. 


THE    DEDUCTIVE    APPROACH  143 

to  be  as  quickly  rejected,  because  of  some  obvious  diffi- 
culty. Again,  a  guess  at  the  meaning  will  indicate  that  a 
certain  word  is  an  accusative,  which  may  be  tested  at 
once  by  a  glance  at  the  word. 

Willmann1  thus  sums  up  the  elements  of  instruction 
by  the  teacher  and  of  study  by  the  student  in  the  teaching 
of  foreign  languages :  — 

1.  Preparation.  —  a.  Hints  by  the  teacher  for  the  stu- 
dent's preparation,    b.  Preparatory  study,    c.  Discussion 
of  the  text  by  the  teacher. 

2.  Translation.  —  a.  Translation    of    the    text    by    a 
student,     b.  Corrections  of  the  same  by  fellow-students 
and  teacher,    c.  Explanations,  mostly  of  logical  and  lin- 
guistic character,  of  what  is  presented  directly  by  the 
text.    d.  Corrected  translation  by  teacher  and  students, 
or  by  students  only. 

3.  Elaboration  of  the  text.  —  a.  Explanation  of  facts, 
references,  etc.,   presented  by  the  author,    b.  Bringing 
out  of  the  ethical  content,     c.  Explanations  of  linguistic 
technique  (poetics,  rhetoric),     d.  Fixing  in  mind  the  lin- 
guistic results  of   the  lesson   (onomatopoeia,  grammar). 
e.  The  results  of  composition  (phraseology,  style). 

While  much  of  the  above  program  of  exercises  pertains 
to  the  giving  or  getting  of  facts,  not  a  little  of  the  work  of 
study  on  the  part  of  the  students  and  of  explanation  on  the 
part  of  the  teacher  is  of  a  deductive  nature,  as,  for  example, 

1  "Didaktik,"  Vol.  II,  p.  415. 


144  SCIENTIFIC    METHOD    IN    INSTRUCTION 

when  the  rules  of  poetics,  grammar,  rhetoric,  etc.,  are 
given  as  a  basis  for  the  conclusions  reached. 

That  there  is  an  important  aesthetic  element  present  in 
the  translation  of  literary  masterpieces  which  has  little  to 
do  with  deductive  processes  is  obvious.  Only  indirectly 
do  rational  processes  lay  the  foundation  for  such  apprecia- 
tion, in  that  they  apply  whatever  canons  of  literary  art  the 
class  may  have  become  possessed  of  in  the  course  of  their 
study.  The  most  prominent  characteristic  of  literary,  as 
of  all  other  art,  is  its  freedom  from  limits.  In  general,  it 
is  restless  under  any  attempt  to  confine  it  by  rules,  for  it 
is  impossible  to  tell  beforehand  just  what  combinations 
will  be  thought  beautiful.  It  is  probable  that  were  a 
strict  set  of  rules  prescribed  for  literary  production,  some 
author  would  successfully  violate  them  all,  for  art  is 
continually  changing,  developing,  adjusting  itself  to  the 
spirit  of  the  age  or  the  sciences  of  humanity.  A  feeling 
of  beauty  with  respect  to  any  literary  product,  however, 
necessarily  passes  over  into  a  judgment  of  beauty.  Es- 
thetic judgment  is  therefore  the  correlative  of  aesthetic 
appreciation  and  is  consequently  implicit  in  all  minds 
capable  of  aesthetic  feeling.  The  literary  artist  helps  it 
into  light.  But  while  aesthetic  feeling  is  creative  in  its 
nature,  impelling  to  action,  taste  is  critical  and  follows 
art.  Taste  attempts  to  say  in  general  what  is  beautiful, 
what  ugly,  and  hence  to  become  a  guide  to  artistic  appre- 
ciation. It  can  judge,  however,  only  by  what  has  been 


THE    DEDUCTIVE    APPROACH  145 

produced.  ^Estheticism  in  literature  is  not  love  of  beauty, 
but  love  of  the  pleasures  of  beauty.  Freely  indulged  in, 
as  in  excessive  novel  reading,  it  leads  to  loss  of  freshness, 
healthiness,  and  vitality  of  aesthetic  feeling.1  The  method 
for  acquiring  aesthetic  appreciation  is  emotional  rather 
than  intellectual,  though  it  must  always  be  recognized 
that  there  is  an  intellectual  basis  to  all  art.  We  learn  to 
appreciate  by  contemplation,  by  direct  observation  and 
insight,  by  looking  for  what  we  are  told  is  there,  and 
especially  by  oral  reading.  The  voice  is  to  literature 
almost  what  the  eye  is  to  painting  and  sculpture,  for  it  is 
the  organ  through  which  the  race  first  learned  to  appre- 
ciate literary  masterpieces  since  they  were  recited  long  be- 
fore they  were  written.  This  must  not  be  taken  to  be  an 
approval  of  the  exclamatory  method  of  exciting  admira- 
tion, for  such  raptures  are  usually  confined  to  the  teacher, 
finding  small  response  in  the  student.  But  a  masterful, 
beautiful,  and  appreciative  reading  of  the  text  under 
favorable  circumstances  is  almost  sure  to  awaken  a  cor- 
responding appreciation  in  the  student.2 

Translation  as  a  method  in  linguistic  study  has  another 
side,  which  will  be  taken  up  under  the  head  of  applica- 
tion, in  the  succeeding  chapter. 

DISCUSSION:  —  i.   Compare  the  deductive  aspects  of  lan- 
guage teaching  with  those  of  mathematics.     2.   What  would 

1  Compare  the  author's  monograph,  "Laboratory  Exercises  in  Art 
Appreciation,"  pp.  12-14,  C.  W.  Bardeen,  Syracuse,  N.Y.,  1908. 

2  Compare  Hiram  Corson,  "The  Voice  and  Spiritual  Education." 


146  SCIENTIFIC    METHOD    IN    INSTRUCTION 

be  lost  were  translation  as  a  set  exercise  abandoned?  3.  Are 
the  ancient  and  the  modern  languages  on  the  same  plane 
with  respect  to  translation? 

75.  It  has  already  been  shown  above  that  deductive 
inference  is  common  in  historical  anticipation.  Though 
it  be  denied  that  history  yields  generalizations  which  are 
both  true  and  important,  and  hence  in  any  specific  sense 
furnishes  a  guide  to  the  future,  yet  here  as  elsewhere  deduc- 
tive application  of  causes  once  established  as  facts  may 
be  and  is  freely  used.  Thus,  much  early  American  history 
becomes  intelligible  when  it  is  once  understood  that  the 
permanent  motives  of  the  French  in  settling  and  ruling 
North  America  were  of  the  type  that  belong  to  a  militant 
monarchy,  where  there  is  absolute  subjection  of  political 
and  religious  individualism;  whereas,  the  motives  of  the 
English,  on  the  other  hand,  were  primarily  industrial  and 
individualistic.  When  Louis  XIV  sent  word  to  Canada 
that  all  heresy  must  be  ruthlessly  stamped  out,  the  gov- 
ernor could  exclaim  with  a  pious  ejaculation,  "There  is 
not  a  heretic  in  all  Canada !"  l  These  motives  become 
causes  of  action  with  the  respective  parties,  and  serve  to 
explain  many  deeds  and  states  of  feeling,  otherwise  inex- 
plicable. In  like  manner  the  objective  purposes  of  a  war, 
a  campaign,  or  a  battle,  serve  to  explain  the  actions  of  an 
army.  When,  for  illustration,  Grant  became  commander- 
in-chief  during  the  Civil  War,  the  campaigns  in  both 

1  John  Fiske,  "  Francis  Parkman,"  in  "A  Century  of  Science,"  p.  220. 


THE    DEDUCTIVE    APPROACH  147 

South  and  East  were  pushed  simultaneously  with  equal 
vigor  in  order,  for  one  thing,  to  prevent  the  transfer  of 
Confederate  forces,  now  from  East  to  South,  now  from 
South  to  East,  as  the  exigencies  of  the  situation  might 
demand. 

On  the  whole,  however,  the  contingent,  or  probable, 
reasoning  of  history  is  concerned  primarily  with  the 
investigations  of  causes  and  effects  of  specific  actions,  and 
only  secondarily  with  the  application  of  principles  to 
explain  or  forecast  events.  The  use  of  deduction  in  appli- 
cation will  be  treated  hi  the  next  chapter. 

DISCUSSION  :  —  Comparison  of  all  three  modes  of  thinking 
in  history:  (i)  Causal  investigation;  (2)  Inductive  approach 
to  generalization;  (3)  Deductive  use  of  principles:  (a)  for 
anticipation,  (6)  for  gaining  new  insight. 

76.  The  natural  sciences,  especially  those  of  a  mathe- 
matical or  semi-mathematical  nature,  yield  much  more 
readily  to  deductive  treatment  than  do  history  and 
literature.  Indeed,  it  may  be  said  that  in  physics,  at 
least,  the  prevailing  custom  of  authors  has  been  to 
present  principles  first,  and  then,  after  more  or  less 
earnest  efforts  to  verify  them,  to  make  deductive  use 
of  them  to  explain  the  phenomena  with  which  the 
subject  deals.  In  botany,  classifications  already  estab- 
lished are  used  deductively  to  identify  new  specimens, 
while  in  the  larger  aspects  of  biology,  broad  general- 


148  SCIENTIFIC    METHOD    IN    INSTRUCTION 

ization  once  derived  serves  to  point  the  way  to  new 
investigations  or  to  clear  up  matters  that  had  for- 
merly been  open  to  more  or  less  surmise. 

Deductive  methods  found  useful  in  physics  and  biology 
serve,  with  more  or  less  modification,  equally  well  in  the 
other  natural  sciences.  By  way  of  summary,  it  may  be 
said  that  the  laboratory,  or  experimental,  method  of 
teaching  natural  science  has  at  least  three  prominent 
aspects.  The  first  of  these  uses  observation  and  ex- 
periment to  lead  up  inductively  to  causes  or  effects, 
to  classifications,  or  to  generalizations.  The  second  uses 
observation  and  experiment  to  verify  general  principles 
which  are  stated  authoritatively  at  the  outset,  in  order 
to  convince  the  student  through  his  own  investigation  that 
they  are  true,  but  chiefly,  it  would  appear,  to  fix  them  more 
vividly  in  his  mind.  Finally,  the  principles  so  presented 
and  so  verified  are  then  used  deductively  to  explain  the 
facts  and  subordinate  principles  of  the  science.  The  third 
purpose  of  the  laboratory  method  is  to  make  the  student 
efficient  in  the  use  of  the  knowledge  thus  gained.  This 
aspect  will  be  treated  under  the  head  of  application. 

DISCUSSION  :  —  The  comparative  serviceability  of  the  de- 
ductive method  of  gaining  new  knowledge  in:  (i)  physics  and 
chemistry;  (2)  botany  and  geology;  (3)  physical  geography 
and  geology;  (4)  physiology  and  hygiene. 


THE    DEDUCTIVE    APPROACH  149 

3.   Processes  of  Application  —  Deduction 

(This  topic  is  treated  in  Chapter  VII  and  is  united  with 
the  corresponding  one  for  induction,  since  the  stage  of 
application  is  the  same  for  both  induction  and  deduc- 
tion.) 


CHAPTER  VII 

PROCESSES  OF  APPLICATION  —  INDUCTION  AND 
DEDUCTION 

77.  Why  does  a  scientific  method  in  the  schoolroom 
call  for  a  special  department  of  'Application,'  when  this 
is  lacking  in  the  methodic  processes  of  the  outside  world  ? 
A  number  of  reasons  growing  out  of  the  conditions  discussed 
in  Sections  44,  45,  and  46  may  be  given.  First,  owing  to 
the  rapidity  of  the  student's  survey  of  race  acquisitions,  his 
knowledge  is  likely  to  be  attenuated  and  meagre,  if  he  but 
touches  the  generalizations,  classifications,  and  causes 
involved  as  he  flits  along  the  panorama  unfolded  by  his 
studies.  He  must  pause,  consider,  test,  and  apply  his  new- 
found insight,  if  it  is  to  have  any  richness  of  content.  One 
reason  why  the  old  linguistic  and  literary  training  as  the 
sole  subject  of  education  satisfied  the  educational  world 
for  so  many  centuries,  was  because  in  this  field  at  least 
the  content  was  rich  and  full,  every  principle  having  a 
thousand-fold  application  to  appropriate  subject-matter. 
However  rich  in  content,  however  closely  related  to  the 
life  of  the  people,  modern  studies  may  seem,  they  will 
never  permanently  satisfy  the  demands  of  education 
until  they,  like  classics  and  mathematics,  also  enrich  the 


PROCESSES    OF    APPLICATION  151 

mind  each  in  its  own  way  with  the  associations  and 
direct  applications  that  can  come  only  from  this  aspect 
of  the  teaching  process. 

Second,  that  which  is  learned  in  skeletonized  form  has 
but  a  transient  hold  upon  the  mind.  Like  a  high-potential 
abstraction  in  metaphysics  to  the  ordinary  man,  a  prin- 
ciple of  human  or  natural  science  apprehended  merely 
by  a  fleeting  glance  soon  takes  its  place  among  that  host 
of  vague  impressions  which,  though  possibly  recognized 
when  mentioned,  perform  no  useful  function  in  actual 
mental  life.  It  is  the  application  of  principles  that  gives 
them  substance,  concrete  embodiment,  and  thus  makes 
them  permanent  dwellers  in  the  mind,  not  mere  transient 
visitors.  A  stage  of  application  is  needed,  therefore,  to 
secure  permanence  of  acquisition. 

The  third  and  most  important  reason  why  a  department 
of  application  is  needed  in  the  teaching  of  any  subject, 
arises  from  the  reciprocal  relation  of  insight  and  efficiency. 
What  indeed  shall  it  profit  a  man  though  he  gain  the  whole 
world  of  knowledge  and  be  not  able  to  use  it?  That  is 
truly  useless  knowledge  which  cannot  be  used.  Educa- 
tion as  revelation  gives  insight;  education  as  application 
gives  efficiency.  The  one  is  as  necessary  as  the  other;  they 
are  the  two  poles  of  the  magnet,  the  two  blades  of  the 
shears,  the  two  parents  of  the  child.  Without  either  the 
other  loses  its  significance.  The  intellectual  mastery  of 
knowledge  gives  us  social  instruments;  its  continuous 


152  SCIENTIFIC    METHOD    IN    INSTRUCTION 

application  to  its  manifold  uses  gives  power  to  use  the 
instruments  effectively  in  society.  The  importance  and 
reciprocal  nature  of  insight  and  efficiency  are  discussed 
from  another  standpoint  in  the  first  volume.1 

78.  To  place  this  stage  of  application  in  still  another 
light,  two  views  in  education  may  here  be  contrasted, 
though  in  practice  they  always  blend  in  varying  proportions. 
They  are  the  psychological  and  the  social.  The  psycho- 
logical aspect  of  education  pertains  to  the  development  of 
the  individual  as  such.  It  is  interested  in  his  personal 
culture,  his  mental  discipline,  his  acquisitions,  his  physical 
perfection,  without  direct  reference  to  society  in  any  of 
its  numerous  forms.  The  microcosm  occupies  the  whole 
field  of  vision  for  one  who  contemplates  education  from 
the  psychological  standpoint  alone.  The  social  view  of 
education  contemplates  the  individual  from  the  standpoint 
of  his  relations  to  his  fellows  in  their  various  groupings, 
civic,  religious,  educational,  economic,  family,  or  social 
in  the  restricted  sense.  The  psychologist  in  education  is 
interested  in  mental  development.  He  lays  the  emphasis 
on  the  subjective  aspect  of  studies,  their  effect  upon  mem- 
ory, imagination,  emotion,  reason,  and  volition,  in  short 
their  value  for  culture  and  discipline.  He  emphasizes  the 
methods  that  rouse  and  interest  the  student,  making  him 
use  his  whole  mind  as  he  acquires  and  thinks,  and  he  re- 
gards those  subjects  as  best  in  education  that  are  most 
1  Ch.  v,  pp.  162-192. 


PROCESSES    OF    APPLICATION  153 

susceptible  to  this  form  of  treatment;  or  if  he  takes  a 
broader  view,  he  recommends  a  combination  of  studies 
that  shall  give  an  adequate  training  in  every  prominent 
type  of  mental  endowment.  It  is  the  psychologist  who 
protests  against  what  he  calls  the  (base)  utilitarian  in 
education,  who  says  that  all  school  subjects,  even  manual 
training  and  domestic  science,  shall  be  purely  'general,' 
in  that  they  but  present  various  ways  of  training  the  mind; 
who  protests  that  all  vocational  training  is  narrow  and 
special,  and  can  be  thought  of  only  when  the  long  period 
of  general,  or  disciplinary  training  is  rounded  out  and 
complete,  presumably  eight  years  from  the  beginning  of 
the  high-school  period.  There  is  validity  in  these  conten- 
tions, and  much  can  be,  as  much  has  been,  said  in  their 
behalf ;  but  they  constitute  only  one  side  of  the  shield. 

The  sociologist  in  education,  on  the  other  hand,  while 
he  too  contemplates  the  individual,  thinks  of  him  as  per- 
forming or  preparing  to  perform  his  various  functions  hi 
society.  Instead  of  emphasizing  a  subjective  mental 
discipline  IL  the  school,  the  sociologist  lays  stress  upon  the 
acquisition  of  skill  that  conduces  to  efficiency  in  the  use  of 
what  is  learned.  Instead  of  choosing  subjects  that  lend 
themselves  easily  to  certain  methods  of  mental  training, 
he  selects  rather  the  subjects  that  relate  most  nearly  to 
the  forms  of  social  efficiency  he  most  highly  regards.  In 
short,  while  the  psychologist  urges  insight  and  mental 
discipline,  the  sociologist  urges  useful  knowledge  and 


154  SCIENTIFIC    METHOD    IN    INSTRUCTION 

trained  efficiency.  It  is,  of  course,  well  known  that  all 
our  great  thinkers  in  education  like  Pestalozzi,  Herbart, 
Froebel,  Huxley,  Harris,  Hall,  and  Dewey  combine,  with 
varying  emphasis  to  be  sure,  these  two  aspects  of  educa- 
tional theory.  These  contrasts  go  to  show,  not  only  the 
great  importance  of  making  the  training  in  efficency  a 
prominent  part  of  all  high-school  methods,  but  they  reveal 
also  the  widely  varying  application  of  the  term.  In  the 
one  case  it  may  mean  anything  that  contributes  to  personal 
development  as  such,  whether  in  volitional,  rational,  or 
aesthetic  relations,  and  in  the  other  it  may  include  the  power 
to  use  knowledge  effectively  in  any  or  all  of  the  groups  that 
constitute  institutional  life,  political,  social,  or  economic. 
The  following  quotation  from  Karl  Pearson  1  contrasts 
the  individualistic  and  the  social  views  from  another 
standpoint :  "  I  fancy  science  will  ultimately  balance  the 
individualistic  and  the  socialistic 2  tendencies  in  evolution 
better  than  Haeckel  and  Spencer  seem  to  have  done.  The 
power  of  the  individualistic  formula  to  describe  human 
growth  has  been  overrated,  and  the  evolutionary  origin 
of  the  socialistic  instinct  has  been  too  frequently  over- 
looked. In  the  face  of  the  severe  struggle,  physical,  and 
commercial,  the  fight  for  land,  for  food,  and  for  mineral 
wealth  between  existing  nations,  we  have  every  need  to 

1  "Grammar  of  Science,"  p.  367. 

1  "Socialistic"  is  here  used  in  its  broad  sense,  and  does  not  refer  to 
what  is  known  as  socialism. 


PROCESSES    OF    APPLICATION  155 

strengthen  by  training  the  partially  dormant  socialistic 
spirit,  if  we  as  a  nation  are  to  be  among  the  surviving  fit 
(hence  the  present  forceful  movement  in  England  and 
America  for  all  sorts  of  industrial  education).  The  im- 
portance of  organizing  society,  of  making  the  individual 
subservient  to  the  whole,  grows  from  the  intensity  of  the 
struggle.  We  shall  need  all  our  clearness  of  vision,  all 
our  reasoned  insight  into  human  growth  and  social  effi- 
ciency in  order  to  discipline  the  powers  of  labor,  to  train 
and  educate  the  powers  of  mind.  This  organization  and 
education  must  largely  proceed  from  the  state,  for  it  is  in 
the  battle  of  society  with  society,  rather  than  of  individual 
with  individual,  that  these  weapons  are  of  service.  Here 
it  is  that  science  relentlessly  proclaims:  A  nation  needs 
not  only  a  few  prize  individuals ;  it  needs  a  finely  regulated 
social  system  —  of  which  the  members  as  a  whole  respond 
to  each  external  stress  by  organized  reaction  —  if  it  is  to 
survive  hi  the  struggle  for  existence." 

DISCUSSION  :  —  Contrast  between  the  social  and  the  psy- 
chological aspects  of  the  educational  theories  of:  i.  Pestalozzi; 
2.  Herbart;  3.  Froebel;  4.  Huxley;  5.  Harris;  6.  Hall; 
7.  Dewey. 

79.  The  forms  which  application  may  take  are  almost 
as  numerous  as  the  studies  themselves  and  the  purposes 
for  which  they  are  taught.  Application  is  a  stage,  now  for 
wide  survey,  as  in  the  tracing  of  historical  causes  and 
effects  or  the  results  of  economic  law,  the  universal  sweep 


156  SCIENTIFIC    METHOD    IN    INSTRUCTION 

of  a  principle  of  conduct,  or  a  generalization  in  evolution; 
now  for  drill  upon  essentials,  translation  of  foreign  lan- 
guages, the  construing  of  words,  oral  and  written  composi- 
tion, or  laboratory,  class-room,  and  workroom  practice  in 
general. 

An  argument  is  made  in  Volume  I1  to  show  that  not 
only  should  the  stage  of  application  be  recognized  in  prin- 
ciple, but  that  a  special  laboratory,  workroom,  or  other 
appropriate  place  should  be  provided  for  each  department 
of  school  study  —  the  mathematical,  the  literary,  the  his- 
torical and  geographical,  no  less  than  the  scientific,  the  in- 
dustrial and  the  artistic.  The  laboratory  or  workroom  is 
now  a  recognized  necessity  in  biology,  physics  and  chem- 
istry, manual  training  and  domestic  science,  drawing  and 
music,  also  for  commercial  courses  and  physical  training. 
It  is  only  formally  lacking  for  languages  and  literature, 
and  for  history,  civics,  geography,  and  economics.  Even 
here  some  provision  is  made,  for  to  a  considerable  extent 
the  library  is  the  true  laboratory  for  certain  aspects  of  these 
subjects,  and  some  schools  have  a  laboratory  for  geography. 
So  nearly  universal  is  the  recognition  of  the  value  of  the 
laboratory,  or  workroom  idea  in  the  realization  of  the 
efficiency  that  should  be  made  to  accompany  insight,  that 
the  modern  high-school  teacher  should  always  seek  to 

1  See  "The  Twofold  Aspect  of  all  School  Studies,"  pp.  162-172,  and 
the  diagram  on  p.  197,  which  shows  how  application,  or  practice,  is  to 
be  provided  in  each  department  of  high-school  study. 


PROCESSES    OF    APPLICATION  157 

secure  its  advantages,  even  if  to  do  so  he  must  from  time 
to  time  transform  his  recitation  room  into  a  laboratory. 

Among  the  most  familiar  and  most  practised  forms  of 
application  as  a  stage  of  method  are  those  almost  uni- 
versally used  in  teaching  mathematics  and  languages. 
Authority,  observation,  and  experiment,  here  as  elsewhere, 
furnish  the  data;  inductive  or  deductive  reasoning  leads 
to  their  comprehension  in  the  form  of  definition,  cause, 
classification,  or  of  generalization  as  seen  in  theorem,  rule, 
formula,  principle,  or  law;  while  application  tests  these 
conclusions  on  new  data,  and  extends  them  to  a  multi- 
tude of  new  cases,  thus  greatly  enriching  the  content  of 
knowledge,  strengthening  the  grasp  upon  fundamentals, 
and,  most  important  of  all,  lifting  insight  to  the  plane  of 
efficiency. 

The  idea  that  education  is  a  true  preparation  for  life 
only  as  it  enables  the  student  to  participate  in  the  life  of 
his  age  and  environment  is  now  accepted  in  principle, 
however  sadly  it  may  fail  in  practice.  The  old  notion  was 
that  real  life  and  school  life  are  necessarily  disparate,  much 
as  Earth  is  sundered  from  Heaven;  that  by  a  rigid  mental 
discipline  on  subjects  which  to  the  student  were  almost 
purely  abstract,  he  could  be  best  prepared  to  meet  the  exi- 
gencies of  that  'life'  which  he  was  by  and  by  to  enter. 
This  doctrine  has  ever  been  the  final  defence  for  lost  or 
losing  causes.  It  supplied  the  argument  for  scholasticism 
when  it  was  being  displaced  by  humanism;  for  classicism 


158  SCIENTIFIC    METHOD    IN    INSTRUCTION 

when  it  was  encroached  upon  by  mathematics;  for  classics 
combined  with  mathematics  when  modern  languages  and 
natural  science  demanded  a  part  of  the  student's  time; 
for  'general'  mental  discipline  when  manual  training 
knocked  at  the  door  of  the  schoolroom;  and  now  echoes 
of  its  protest  are  heard  when  vocational  and  industrial 
training  in  general  are  proposed,  that  education  may  once 
more  prepare  the  student  for  life  by  making  him  even  dur- 
ing his  school  days  a  true  participant  in  it.  In  all  genuine 
education,  mental  discipline,  like  culture  itself,  is  a  neces- 
sary concomitant.  "Algebra  conquers  adipose;"  geome- 
try necessitates  clear  thought ;  to  comprehend  a  play  of 
Shakespeare  is  to  rise  to  higher  levels  of  insight  and 
feeling;  to  master  a  law  of  nature  elevates  both  mind  and 
heart.  We  need  not  fear  that  education  animated  by 
living,  vital,  urgent  motives  will  lack  any  of  the  good 
characteristics  naturally  inhering  in  the  mastery  of  a  sys- 
tem of  thought.  So  far  from  lacking  any  of  them,  it  will 
rather  add  new  ones,  and  will  throw  over  all  a  charm  as 
old  as  life  itself,  of  which  it  is  begot. 

The  laboratory,  the  shop,  the  workroom,  is  at  once  the 
vestibule  of  the  school  and  the  anteroom  to  factory,  count- 
ing-room and  office.1  It  is  a  place  where  the  noise,  bustle, 
and  urgent  purpose  of  the  one  may  enter,  without  destroy- 
ing the  opportunity  for  the  mental  operations  of  the  other. 
In  it  the  student  may  share  in  the  thought-life  of  the 

1  See  Schematic  Outline,  Vol.  I,  p.  197. 


PROCESSES    OF    APPLICATION  159 

outer  world,  may  reproduce  its  activities,  without  being 
swept  into  the  whirl  of  competition  or  having  his  ener- 
gies narrowed  to  a  single  channel  by  the  pressure  of 
economic  necessity.  In  the  workroom,  the  inner  life  may 
come  into  touch  with  the  outer,  share  in  its  motives,  and 
be  quickened  into  vitality  by  its  influence,  without  being 
diverted  from  its  leading  purposes,  which  are  mental 
growth,  ethical  development,  and  practical  efficiency. 

DISCUSSION  :  —  Phases  of  outside  life  to  which  each  of  the 
high-school  studies  is  vocationally  most  closely  related. 

80.  Translation  as  an  exercise  in  application  gives  con- 
stant practice  hi  applying  the  known  laws  of  grammar  and 
rhetoric  to  the  foreign  text.  It  renders  the  mind  quick  to 
see  and  appreciate  not  only  broad  but  also  subtle  distinc- 
tions of  thought.  Its  constant  practice  of  requiring  ade- 
quate English  terms  to  express  the  thought  of  the  author 
enriches  the  diction  of  the  student  at  a  rapid  rate.  It  is 
a  common  observation  that  a  classical  scholar  never  lacks 
for  words  to  express  his  ideas.  Whatever  advantages 
there  may  be  in  translation  are  accented  and  multiplied 
and  rendered  permanent  by  the  iteration  of  years.  But 
by  the  same  token,  its  faults  are  likely  to  have  a  like  endur- 
ing quality.  If  it  permits  slipshod  'translation  English' 
in  which  native  is  subordinated  to  foreign  idiom;  if  it 
tends  to  the  decay  of  original  thought  through  devotion 
to  the  thought  of  others;  if  it  turns  the  mind  permanently 


l6o  SCIENTIFIC    METHOD    IN    INSTRUCTION 

to  bygone  events  having  small  relation  to  the  present, 
then  its  unquestioned  advantages  in  producing  the  liber- 
ated tongue,  are  offset  by  a  formidable  list  of  actual  dis- 
advantages, to  say  nothing  of  a  possible  waste  of  time  and 
mental  effort.  The  maxim  of  the  Latin  teacher  should  be : 
through  Latin  to  English;  through  ancient  to  modern  life. 

Every  writer  on  the  art  of  translation  protests  vigorously 
against  that  'jargon'  which  so  easily  besets  the  student  as 
he  tries  to  render  in  comprehensible  English  the  meaning 
of  the  foreign  text.  Thus  Wilhelm  Munch  in  his  Kunst 
des  Uebersetzens  aus  dem  Franzossischen,  says,  "There  has 
arisen  in  translation  a  jargon  which  advances  in  an  inflexible 
armor  that  is  peculiarly  foreign."  "It  behooves  every 
teacher  of  the  classics,"  says  Lattmann,  "to  banish  this 
'  school  jargon.' " 

The  nature  of  the  training  for  efficiency  that  comes 
from  translation  is  vividly  presented  in  the  following  cita- 
tions from  authors  who  have  written  upon  this  topic. 

Here  is  a  voice  that  comes  down  to  us  from  a  hundred 
years  ago,1  telling  us  the  essentials  of  good  work  in  transla- 
tion: "I  would  describe  a  good  translation  to  be  that  in 
which  the  merit  of  the  original  work  is  so  completely  trans- 
fused into  another  language  as  to  be  as  distinctly  appre- 
hended, and  as  strongly  felt,  by  a  native  of  the  country 
to  which  that  language  belongs,  as  it  is  by  those  who  speak 
the  language  of  the  original  work.  Now,  supposing  this 

1  Alex.  Eraser  Tytler,  "Principles  of  Translation,"  1812. 


PROCESSES    OF    APPLICATION  l6l 

description  to  be  a  just  one,  which  I  think  it  is,  let  us  exam- 
ine what  are  the  laws  of  translation  which  may  be  deduced 
from  it.  It  will  follow:  — 

"i.  That  the  translation  should  give  a  complete  tran- 
script of  the  ideas  of  the  original  work. 

"2.  That  the  style  and  manner  of  writing  should  be  of 
the  same  character  with  that  of  the  original. 

"3.  That  the  translation  should  have  all  the  ease  of 
original  composition." 

Tolman,1  in  his  "Art  of  Translating,"  a  work  based  upon 
Cauer's  Die  Kunst  des  Uebersetzens,  quotes  approvingly 
the  following  paragraph  from  his  master:  "A  double  task 
confronts  the  translator ;  first  the  language  with  which  he 
translates  must  be  genuine  living  English,  not  an  artificial 
Grecized  or  Latinized  English ;  else  how  can  it  come  near 
to  our  feelings?  In  the  second  place,  the  peculiar  style 
of  the  old  poet  or  author  must  be  preserved.  Homer 
must  be  translated  into  different  English  from  Virgil, 
Tacitus  from  Cicero.  For  the  first  task  the  translator 
must  have  mastery  over  his  own  language.  For  the  sec- 
ond, the  translator  must  breathe  the  spirit  of  his  author 
and  from  that  standpoint  build  his  English  sentence." 

Concerning  the  function  of  Latin  translation  as  a 
training  in  English,  Bennett2  writes  as  follows:  — 

1  Herbert  Cushing  Tolman,  "The  Art  of  Translating,"  p.  5,  B.  H. 
Sanborn  &  Co.,  Boston,  1901. 

8  Charles  E.  Bennett,  in  "The  Teaching  of  Latin  and  Greek"  (Bennett 
and  Bristol),  pp.  11-12,  Longmans,  N.Y. 

M 


1 62  SCIENTIFIC    METHOD    IN    INSTRUCTION 

"First  and  foremost,  I  should  say  Latin  is  of  value  be- 
cause it  confers  a  mastery  over  the  resources  of  one's 
mother-tongue.  This  mastery  is  the  direct  and  necessary 
result  of  careful  daily  translation,  —  a  process  involving 
on  the  one  hand  a  careful  consideration  and  analysis  of 
the  thought  of  the  author  read,  and  on  the  other  a  severe 
and  laborious  comparison  of  the  value  of  alternative 
English  words,  phrases,  and  sentences,  with  the  consequent 
attainment  of  skill  in  making  the  same  effective  as  vehicles 
of  expression.  .  .  .  Translation  is  a  severe  exercise. 
The  lexicon  or  vocabulary  tells  the  meaning  of  words,  the 
grammar  states  the  force  of  inflected  forms;  but  it  is  only 
after  the  pupil,  provided  with  this  equipment,  has  attacked 
his  Latin  sentence  with  a  view  to  translation  that  the  real 
struggle  begins.  His  vocabulary  has  given  him  a  dozen  or 
even  twenty  meanings  under  a  single  verb  or  noun,  and 
the  pupil  must  reflect  and  nicely  discriminate  before  he 
can  choose  the  right  word,  the  one  just  suited  to  the  context. 
Further,  his  Latin  sentence  may  be  long,  complex,  and 
periodic,  entirely  different  from  anything  we  know  in 
English.  Such  a  sentence  must  be  broken  up  and  so 
arranged  as  to  conform  to  our  English  mode  of  expression; 
or  the  Latin  sentence  may  have  one  of  those  Protean  abla- 
tive absolutes,  —  an  idiom  that  our  English  style  prac- 
tically abhors.  Every  such  ablative  absolute  has  to  be 
examined  with  care  prior  to  an  English  rendering.  It  may 
express  time,  cause,  concession,  condition,  attendant  cir- 


PROCESSES    OF    APPLICATION  163 

cumstance,  means,  or  what  not,  and  must  be  rendered 
accordingly.  Again,  the  Latin  sentence  may  secure  by  its 
arrangement  of  words  certain  effects  of  emphasis  which 
English  can  bring  out  only  by  the  employment  of  very 
different  resources." 

From  the  foregoing  exposition  and  quotations  it  is  suffi- 
ciently apparent  that  practice  in  translation,  an  art  ap- 
proved for  many  centuries  by  nearly  all  teachers  of  lan- 
guage, is  a  significant  form  of  application,  serving  several 
purposes,  chief  of  which  are:  (i)  drill  in  the  use  of  lin- 
guistic rules  and  principles,  and  (2)  practice  in  varied  and 
facile  use  of  the  mother-tongue. 

DISCUSSION: — i.  How  best  prevent  the  habit  of  using 
'jargon'  English  in  translation.  2.  Possibility  of  securing 
equivalent  training  in  the  application  of  grammar  and  rhetoric 
without  translation. 

81.  The  art  of  composition  in  foreign  languages  belongs 
almost  entirely  to  the  stage  of  application,  whether  with 
Bennett  we  conceive  this  exercise  to  be  a  drill  in  grammar, 
or  whether,  as  in  the  modern  foreign  languages,  we  con- 
ceive the  purpose  of  the  composition  to  be  facility  in  the 
use  of  the  language  as  a  means  of  expression  and  inter- 
communication. 

Bennett  says:  "What,  then,  is  the  purpose  and  function 
of  Lathi  composition  in  the  school  ?  So  far  as  reason  and 
experience  enable  me  to  judge,  the  study  of  Latin  com- 
position is  primarily  intended  to  increase  the  accuracy, 


164  SCIENTIFIC    METHOD    IN    INSTRUCTION 

breadth,  and  certainty  of  the  pupil's  grammatical  knowl- 
edge —  more  particularly  his  knowledge  of  syntax.  He 
first  learns  the  Subjunctive  of  Purpose,  let  us  say,  or  the 
Gerundive  construction,  by  learning  to  recognize  these 
idioms  when  he  meets  them  in  his  reading.  But  this  is 
only  partial  knowledge.  A  completer  knowledge  of  the 
Subjunctive  of  Purpose  or  the  Gerundive  construction  is 
required  when  the  pupil  learns  to  employ  these  in  actual 
phrases  of  his  own  making.  He  then  sees  these  construc- 
tions from  a  new  side,  and  a  practical  side.  The  act  of 
constructing  sentences  which  contain  these  fixes  his  mind 
more  intently  upon  the  construction  than  ever  before. 
His  knowledge  of  it  is  fuller  and  surer.  Hence  it  is  pri- 
marily as  a  contributory  to  a  better  knowledge  of  the 
grammar,  that  the  study  of  Latin  composition  is  of 
value."  l 

This  position  is  clear  and  definite,  and  is  ably  defended  in 
the  pages  that  follow.  The  only  point  to  be  made  here  is 
that  such  an  exercise  in  composition  is  wholly  a  deductive 
exercise  in  the  application  of  grammatical  principles,  de- 
signed to  fix  knowledge  and  to  make  the  student  efficient 
in  the  use  of  it. 

The  rival  theory,  that  represented  by  Collar  and  Dan- 
iell,  is  a  modification  of  the  method  of  connected  composi- 
tion recommended  by  Ascham 2  and  practised  with  so  much 

1  "The  Teaching  of  Latin  and  Greek,"  pp.  160,  161. 
8  "Scholemaster." 


PROCESSES    OF    APPLICATION  l6$ 

success  by  Jacotot.1  It  seeks  to  secure  continuous  dis- 
course in  composition  by  basing  the  exercises  upon  the 
text  which  the  class  is  reading.  This  is  effected  by  re- 
quiring the  student  to  put  into  Latin  again,  a  somewhat 
altered  English  translation  of  the  original.  The  changes 
are  those  of  number,  person,  tense,  mode,  etc.,  and  are 
introduced  as  the  student  is  able  to  make  them.  Jacotot's 
maxim  for  work  of  this  kind  is  expressed  as  follows: 
''Learn  by  heart,  and  understand,  the  first  six  books  of 
Tele"maque,  or  an  equivalent  portion  of  any  eligible  work 
in  the  language  to  be  acquired,  and  repeat  it  incessantly. 
Refer  everything  else  to  this,  and  you  will  certainly  learn 
the  language."  His  exercises  in  composition  are  based 
on  the  maxim,  All  is  in  all,  and  the  pupil  is  expected  to 
justify  his  use  of  words,  phrases,  and  constructions  by 
referring  them  to  the  text  he  has  committed  to  memory. 
"It  is  because  All  is  in  all,  that  the  precept,  'Learn  some- 
thing thoroughly  and  refer  everything  else  to  it,'  leads  in 
practice  to  results  so  astonishing  as  those  which  are  the 
proud  trophies  of  the  Universal  Instruction."  2 

Composition  in  continuous  discourse  based  on  the  text 
of  an  author  is,  like  that  for  grammatical  drill,  still  an  exer- 
cise in  the  application  of  what  has  been  learned. 

DISCUSSION  :  —  Comparison    of    the    arguments    for    and 

1  See  exposition  by  Joseph  Payne,  "Lectures  on  Education,"  pp.  341- 
386. 

1  Idem,  p.  379. 


1 66  SCIENTIFIC    METHOD    IN    INSTRUCTION 

against   the   two   purposes   of   composition:     i.  In   ancient 
languages;    2.  In  modern  foreign  langauges. 

82.  Whatever  composition  in  English  may  be,  it  is  not 
a  parade  ground  for  drill  in  grammar.  Its  leading  pur- 
pose is  facility  and  excellence  in  the  use  of  written  English. 
That  the  principles  of  grammar  and  rhetoric  are  valuable 
means  in  the  accomplishment  of  this  purpose  is  a  matter 
of  course.  For  the  most  part,  however,  they  are  applied 
instinctively,  and  certainly  never  become  the  end  for  which 
the  exercise  is  written.  Yet  written  and  oral  composition 
are  peculiarly  the  field  of  application  for  all  that  properly 
goes  under  the  head  of  'English.'  It  is  here  that  the 
student  is  incited  to  think  for  himself,  to  imitate  good 
authors  in  form,  while  supplying  fresh  original  thought. 
One  who,  for  instance,  tries  his  hand  at  imitating  Portia's 
apostrophe  to  Mercy  by  making  a  similar  one  on  Justice, 
will  have  ample  scope  for  invention  even  in  his  imitation, 
and  certainly  will  not  lack  opportunity  and  incentive  for 
original  thinking.  It  is  the  biographical  testimony  of 
many  celebrated  writers  that  they  taught  themselves  to 
write  by  practising  exercises  like  the  above,  in  which  an 
admired  literary  form  is  applied  as  well  as  possible  to 
original  matter.  Thus  far  in  our  schools  we  have  assumed 
that  composition  is  purely  an  individual  affair,  like  eating 
or  dying,  when  it  comes  to  the  work  of  composing;  that 
cooperative  effort  here  is  either  impossible  or  illegitimate. 
But  if  a  class  may  together  prepare  for  writing,  why  may 


PROCESSES    OF    APPLICATION  167 

not  small  groups  work  together  to  advantage  at  the  real 
composition?  Here  the  need  for  a  room  which  may  for 
the  time  being,  at  least,  become  a  real  laboratory,  or 
literary  workshop,  is  felt.  The  library  can  hardly  become 
such  a  place,  for  its  chief  rule  is  silence.  A  literary  work- 
shop should  be  a  place  where  small  cooperating  groups 
may  consult  together,  and  together  work  out  their  results, 
first  one  and  then  another  acting  as  amanuensis  for  the 
group.  They  should  have  at  hand  the  needed  materials  in 
the  way  of  dictionaries,  grammars,  rhetorics,  standard 
works  on  style,  and  especially  copies  of  the  best  writings 
of  the  kind  they  are  trying  to  produce.  Such  works,  like 
Scott  for  description,  can  be  supplied  from  time  to  time 
from  the  library  as  they  are  needed.  The  students  may 
immerse  themselves  for  hours  or  days,  if  need  be,  in  the 
kind  of  writing  they  propose  to  attempt.  Such  work 
may  at  least  be  cooperative,  even  if  the  first  draft  be  made 
individually  by  each  student,  to  be  afterward  combined 
into  a  single  production  by  the  group.  Premature,  hence 
immature,  fruit  is  the  kind  usually  produced  by  the 
young  literary  plant,  for  it  tries  to  bear  when  it  should 
be  just  growing,  or  at  most  only  blossoming.  Even  if 
the  work  of  composition  is  still  to  be  considered  a 
purely  individual  affair,  the  laboratory  or  workroom 
should  nevertheless  be  provided  where  books  may  be 
freely  consulted,  and  where  the  student  may  move  freely 
from  place  to  place,  stand  or  sit  as  he  prefers,  and  as 


1 68  SCIENTIFIC    METHOD    IN    INSTRUCTION 

freely  consult  the   elbow-to-elbow  teacher  who  presides 
over  the  whole.1 

The  literary  workshop  should  also  become  the  genera- 
ting plant  for  oral  composition,  in  which  one  after  another 
the  students  may  try  their  hands  at  continuous  narration 
or  exposition.  Any  literary  work  —  say  Mark  Twain's 
"The  Prince  and  the  Pauper"  —  may  be  carefully  read 
and  reduced  to  brief  outline  by  cooperative  work,  one  per- 
son taking  perhaps  a  single  chapter  for  oral  reproduction, 
illustrated,  it  may  be,  with  blackboard  drawings.  As 
chapter  after  chapter  is  thus  given  in  oral  speech,  which 
will  soon  become  fluent  and  measurably  correct,  the 
interest  of  all  will  be  secured,  and  cooperative  criticism 
as  to  omissions,  unwarranted  additions,  deviations,  mis- 
conceptions, or  failure  to  express  the  animating  spirit  of 
the  author,  and  occasional  slips  in  pronunciation  and 
grammar,  will  be  a  stimulus  to  effort,  while  appreciative 
listening  will  lend  reality  and  vividness  to  the  whole 
exercise.  Out  of  such  practice  as  much  writing  may 
spring  as  teacher  or  pupil  desires.  Certainly  from  it 
we  may  expect  a  loosened  tongue  and  a  quickened 
mind.2 

1  For  an  inspiring  article  on  one  form  of  literary  appreciation  and 
expression,  see  M.  Catherine  Mahy,  "^Esthetic  Appreciation  of  Litera- 
ture in  Secondary  Education,"  The  School  Review,  December,  1907, 
pp.  731-743- 

1  Compare  Carpenter,  Baker  &  Scott,  "The  Teaching  of  English," 
pp.  244-249. 


PROCESSES    OF    APPLICATION  169 

DISCUSSION:  —  Other  means  of  enhancing  the  value  of  oral 
and  written  composition  in  English.1 

83.  The  laboratory  is  now  well  established  as  an  indis- 
pensable means  of  instruction  in  practically  all  the  natural 
sciences,  also  in  commercial  courses  and  the  practical 
aspects  of  industrial  training.  It  serves  at  least  three 
important  functions.  They  are :  — 

1.  To  enable  the  student  to  acquire  first-hand  knowl- 
edge by  observation  and  experiment. 

2.  To  enable  him  to  discover  or  deduce  causes,  classi- 
fications, or  generalizations  by  inductive  processes;  also, 
on  the  other  hand,  to  verify  them  when  given  or  found, 
and  to  use  them  deductively  to  solve  problems  or  to  ex- 
plain facts  and  subordinate  principles. 

3.  Finally  to  give  the  student  incentive  and  opportunity 
to  apply  his  new-found  knowledge  upon  a  multitude  of 
new  cases,  that  it  may  acquire  richness  of  content,  be 
firmly  fixed  in  the  mind  through  much  use,  and  finally 
that  the  student  may  by  means  of  it  rise  to  new  levels  of 
efficiency. 

It  may  safely  be  asserted  that  no  other  didactic  inven- 
tion of  modern  times  has  the  educational  significance  of 
the  laboratory,  for  it  has  vivified  the  learning  of  facts, 
quickened  the  processes  of  thinking,  giving  them  incentive, 
guidance,  concreteness,  and  vitality,  and  greatly  heightened 

Consult  Buck,  "Laboratory  Method  in  Teaching  English,"  Pro- 
ceedings N.E.A.,  1004,  pp.  506-508;  also  Percival  Chubb,  "The  Teach- 
ing of  English,"  pp.  170,  222. 


170  SCIENTIFIC    METHOD    IN    INSTRUCTION 

the  capacity  of  the  student  to  use  in  daily  life  the  insight 
he  has  gained.  Laboratory  is  indeed  a  word  to  conjure 
with;  yet  like  all  instruments  in  human  hands,  it  is  ca- 
pable of  defeating  the  ends  it  was  devised  to  serve.  Its 
exercises  may  become  as  perfunctory,  as  arid,  as  any 
performed  by  old-time  methods,  for  even  here  it  is  quite 
possible  for  the  student  to  lose  sight  of  all  relations  to 
life  and  to  spend  his  time  upon  a  set  of  scholasticized 
exercises  wholly  devoid  of  living  motives.  Under  such 
circumstances  science  passes  from  life  to  death;  students 
lose  their  interest  in  it  and  drop  out  of  its  classes,  thinking 
it  to  be  dull  and  tedious.  On  the  other  hand,  nothing  is 
more  inspiring  than  laboratory  practice  when  efficiency 
is  being  gained  in  real  things.  Thus,  for  illustration,  the 
physics  laboratory  may  be  stocked  with  discarded  machines 
of  the  mechanical  world.  Many  a  machine  that  is  now 
sent  to  the  scrap  heap  might  serve  a  useful  purpose  in  the 
physical  laboratory.  Think  of  the  many  devices  for  using 
the  electric  current  for  light,  heat,  motion;  of  the  manifold 
internal-combustion  motors  that  fill  the  market,  whether 
for  use  on  land  or  on  water.  One  Y.  M.  C.  A.  establish- 
ment in  New  York  City  gathered  in  a  class  of  eight  hun- 
dred young  men  and  boys  and  held  them  for  months  upon 
the  automobile  engine.  The  genuine  attracts;  the  arti- 
ficial repels.  The  commercial  laboratories  should  be  able 
to  draw  abundant  materials  from  the  museum  of  com- 
mercial products,  such  as  the  collections  supplied  to  the 


PROCESSES    OF    APPLICATION  171 

high  schools  of  Pennsylvania  by  the  Philadelphia  Museums, 
for  in  this  way  their  laboratory  practice  catches  the  spirit 
of  the  real  world  of  business.  Manual  training  shops  may 
double  their  usefulness  by  permitting  the  students  to  make 
whole  things  rather  than  fragments  of  things,  and  when 
possible  to  invent  and  construct  that  which  may  find  a 
real  use  in  home  or  school.  At  present  much  of  this 
practice  is  highly  artificial,  and  hence  out  of  touch  with 
the  industrial  world.  Aside  from  keeping  the  hands  busy 
and  furnishing  a  needed  relief  from  the  more  highly  in- 
tellectual exercises  of  the  school,  it  performs  but  a  fraction 
of  its  real  function.  Certainly  most  of  the  boys  of  the 
elementary  schools  who  go  to  work  without  attending  the 
high  school  must  join  the  ranks  of  unskilled  labor,  even 
though  they  take  the  conventional  manual  training  offered. 
This  course  is,  moreover,  so  meagre  in  content,  so  formal 
and  artificial  in  character,  so  restricted  hi  amount,  that  it 
does  not  even  encourage  the  boys  to  take  more  of  it  hi  the 
high  school  in  order  to  fit  themselves  for  practical  occupa- 
tions. Such  institutions  are  described  as  "Schools  with 
shops  attached,"  whereas  for  the  good  of  the  mass  of  boys 
they  should  be  "Shops  with  schools  attached."  A  boy 
does  not  have  to  cease  to  think  when  he  goes  into  a  manual 
training  department;  he  merely  learns  to  think  in  a  more 
concrete,  more  effective  way.  He  gains  efficiency,  not 
only  through  increased  skill  of  hand,  but  also  through 
the  awakening  of  fertility  in  device  to  meet  difficulties. 


172  SCIENTIFIC    METHOD    IN    INSTRUCTION 

If  regulation  clamps  are  not  at  hand,  home-made  ones 
must  be  devised;  if  a  piece  of  oak  for  a  chair  back  re- 
fuses to  bend  into  the  proper  shape  around  pegs,  even 
after  being  steamed  or  boiled,  it  will  easily  yield  if  put 
into  the  vise  with  a  piece  of  wood  behind  each  end. 

In  short,  the  laboratory  as  a  place  for  the  application 
of  scientific  or  technical  knowledge  performs  its  true 
function  in  a  high  degree  only  when  it  is  animated  by 
motives  drawn  from  the  throbbing  life  of  the  world  just 
outside  the  school,  just  around  the  corner.  If  the  labora- 
tory work  is  the  application  of  pure  science,  then  the  pupils 
must  utilize  the  objects  which  science  has  produced,  and 
must  try  to  solve  its  real  problems  —  they  must  work  with 
engines  and  apparatus  in  physics;  solve  live  problems  in 
chemistry ;  handle  real  plants,  the  products  of  the  fields, 
in  botany;  use  the  actual  materials  of  commerce  in  the 
commercial  laboratory  courses,  and  so  on.  If  it  consists 
of  manual  training  exercises,  the  student  must  produce 
wholes  instead  of  mere  fragments,  spend  time  enough  to 
effect  real  efficiency,  and  put  its  products  to  use,  not  throw 
them  away  or  burn  them  up. 

The  details  of  laboratory  work  suitable  to  the  several 
studies  are  well  set  forth  in  the  newer  works  upon  the 
teaching  of  these  studies  in  the  high  school.1 

DISCUSSION:  —  i.  Amount  of  time  desirable  for  laboratory 
application.    How  secured  ?    2.  Means  of  making  the  labora- 

1  See  the  Hst  of  such  works  cited  above  on  p.  84. 


PROCESSES    OF    APPLICATION  173 

tory  the  connecting  link  between  the  school  and  the  industrial 
world. 

84.  The  time-honored  custom  of  all  mathematical 
teachers  has  been  to  secure  what  they  regarded  as  adequate 
practice  in  the  application  of  the  rules  and  principles  of 
algebra,  geometry,  and  trigonometry,  by  requiring  the 
student  to  solve  a  large  number  of  exercises  involving  the 
use  of  these  generalizations.  Even  in  the  so-called  '  read- 
ing' of  mathematics  the  student  must  read  ever  with 
pencil  in  hand  ready  to  write  out  every  exercise  inserted 
for  illustration  and  practice.  DeMorgan  l  discusses  this 
point  as  follows:  — 

"  The  first  thing  to  be  attended  to  in  the  reading  of  any 
algebraic  treatise,  is  the  gaining  a  perfect  understanding 
of  the  different  processes  there  exhibited,  and  of  their 
connection  with  one  another.  This  cannot  be  attained  by 
a  mere  reading  of  the  book,  however  great  the  attention 
which  may  be  given.  It  is  impossible  by  reading  in 
mathematical  work  to  fill  up  every  process  in  the  manner 
in  which  it  must  be  filled  up  in  the  mind  of  the  student 
before  he  can  be  said  to  have  completely  mastered  it. 

"  The  method  we  recommend  is  to  write  the  whole  of  the 
symbolical  part  of  each  investigation,  filling  up  the  parts 
to  which  we  have  alluded,  adding  only  so  much  verbal 
elucidation  as  is  absolutely  necessary  to  explain  the  con- 
nection of  the  different  steps,  which  will  generally  be  much 

1  "The  Study  and  Difficulties  of  Mathematics,"  pp.  175,  176. 


174  SCIENTIFIC    METHOD    IN    INSTRUCTION 

less  than  what  is  given  in  the  book.  This  may  appear  an 
alarming  labor  to  one  who  has  not  tried  it,  nevertheless 
we  are  convinced  that  it  is  the  shortest  method  of  pro- 
ceeding, since  the  deliberate  consideration  which  the  act  of 
writing  forces  us  to  give,  will  prevent  the  confusion  and 
difficulties  which  cannot  fail  to  embarrass  the  beginner 
if  he  attempts,  by  mere  perusal  only,  to  understand  new 
reasoning  expressed  in  new  language."  Again  he  says, 
"On  arriving  at  any  new  rule  or  process,  the  student  should 
work  a  number  of  examples  sufficient  to  prove  to  himself 
that  he  understands  and  can  apply  the  rule  or  process 
in  question."  It  is  this  constant  practice  in  application 
that  has  placed  side  by  side,  translation  in  language  and 
the  solving  of  examples  in  mathematics,  as  the  two  sover- 
eign recipes  for  the  training  of  mind.  They  have  been  — 
perhaps  still  are  —  the  greatest  instruments  in  the  hands  of 
the  schoolmaster  for  effecting  mental  discipline.  Naturally 
the  two  processes  differ  in  character  and  effect.  The 
supreme  excellence  of  the  latter  is  that  the  exercises  in 
mathematics  may  be  almost  perfectly  graded  in  difficulty 
to  suit  the  expanding  power  of  the  youthful  mind,  and  like 
exercises  in  translation,  may  be  limited  or  extended  in 
amount  at  will.  Furthermore,  there  is  in  this  subject 
always  a  tangible  and  ever-advancing  fulcrum  for  the 
overcoming  of  difficulties,  and  which  if  once  lost  may  be 
recovered  by  review  or  further  reflection.  He  who  con- 
templates the  advantages  of  mathematics  as  an  instrument 


PROCESSES    OF    APPLICATION  175 

of  intellectual  training  may  well  become  enamoured  of  its 
perfection  —  a  subject  in  which  definite  tasks  may  be 
assigned,  and  definite  results  attained;  perfectly  elastic 
as  to  quantity  of  assignment,  capable  of  being  exactly 
regulated  hi  difficulty,  and  furnishing  incentive  and  op- 
portunity for  the  acquisition  of  the  highest  degree  of  skill 
in  its  application.  It  is  not  strange  that  many  a  teacher, 
believing  mental  discipline  to  be  the  end  of  education, 
should  exclaim,  "  Tarry  here  !  We  shall  never  find  any- 
thing better ! "  He  would  be  right,  were  number  the  whole 
of  life. 

Completely  as  the  writing  out  of  exercises  in  mathe- 
matics has  seemed  to  meet  the  demands  of  application, 
teachers  in  this  subject  have  devised  a  new  means  of 
making  this  stage  of  method  still  more  complete.  A 
part  of  what  is  now  known  as  the  'Laboratory  method' 
gives  a  new  scope  to  exercises  of  this  character.  This 
movement,  starting  with  an  address  by  John  Perry,  of 
England,  in  1901,  has  been  vigorously  discussed  in  this 
country  by  such  men  as  Professors  Moore,  Myers,  and 
Young.  A  full  bibliography  of  the  subject,  together  with 
an  extended  exposition  of  the  movement,  is  found  hi  Young's 
book  on  "  The  Teaching  of  Mathematics."  1  Much  of 
this  new  work  pertains  to  the  acquisition  of  mathe- 

1  J.  W.  A.  Young,  "The  Teaching  of  Mathematics  in  the  Elementary 
and  the  Secondary  School,"  pp.  87-121.  Longmans,  Green,  &  Co.,  N.Y., 
1907. 


176  SCIENTIFIC    METHOD    IN    INSTRUCTION 

matical  knowledge  and  insight  through  methods  and  with 
materials  that  appeal  to  the  senses.  Graphical  methods 
are  employed,  and  various  modes  of  proof  are  admitted, 
such  as  those  which  are  based  on  intuition,  on  measure- 
ment, the  free  use  of  motion,  and  on  what  the  eye  can  see. 
Such  implements  as  the  following  are  freely  employed: 
models,  slide-rules,  surveying  instruments,  balances, 
steelyards,  pendulums;  levers,  pulleys,  wedges,  screws, 
vises;  mercurial  barometer,  thermometer,  instruments 
for  measuring  specific  gravity,  and  the  like. 

The  field  of  application  in  this  new-found  laboratory  is 
the  constant  exemplification  of  mathematical  truths  as 
they  are  more  or  less  concretely  applied  to  the  natural 
sciences,  especially  physics,  a  list  of  such  exercises  being 
assigned  to  the  students,  though  not  necessarily  for  si- 
multaneous performance.  Comparing  the  mathematical 
with  the  physical  laboratory,  Young  discusses  the  subject 
as  follows:  — 

"In  Mathematics  the  situation  is  much  better.  The 
possibility  of  doing  much  work  with  the  class  as  a  unit  is 
one  of  the  great  advantages  of  the  mathematical  subject- 
matter,  and  it  is  to  be  cherished  with  the  deepest  solici- 
tude, and  not  to  be  abandoned  because  of  a  mere  analogy. 
The  apparatus  needed  for  mathematics  (pencil  and  paper 
the  most  prominent)  can  be  improvised  by  the  pupil  as 
a  rule,  and  it  is  quite  possible  to  arrange  matters  so  as  to 
retain  the  benefits  of  the  class  system,  and  add  thereto  the 


PROCESSES    OF    APPLICATION  177 

good  features  of  the  physical  laboratory  system,  while 
avoiding  its  defects."  * 

Thus  one  more  step  is  taken  toward  making  the  work- 
shop idea  universal  hi  the  high  school. 

DISCUSSION  :  —  i.  Extent  to  which  pure  science  and  mathe- 
matics in  the  high  school  should  become  applied  science  and 
mathematics.  2.  Advantages  and  limitations  of  laboratory 
practice  in  mathematics. 

1  "The  Teaching  of  Mathematics,"  p.  119. 


CHAPTER   Vin 
COMBINATIONS  AND  VARIATIONS 

i.  The  Heuristic  Method 

85.  The  word  heuristic  (Gr.  heurisko,  to  find  out)  is 
somewhat  new  in  educational  terminology,  but  expresses 
a  familiar  idea ;  namely,  that  the  student  be  placed  in  the 
attitude  of  a  discoverer,  that  he  be  set  to  finding  out  things 
for  himself.  These  things  are  of  diverse  character,  but 
fall  into  the  following  chief  divisions :  — 

1.  The  discovery  of  essential  facts  in  a  lesson,  say,  on 
history,  literature,  or  science. 

2.  The  discovery  of  the  cause  of  a  phenomenon,  of 
what  will  happen  in  the  case  of  a  supposed  cause,  or  of  the 
law  or  principle  according  to  which  a  given  set  of  phe- 
nomena are  controlled. 

3.  The  finding  out  of  "witty  inventions"  in  order  to 
solve  adequately  by  physical  devices  a  problem  presented 
by  supposition  or  by  an  actual  situation. 

Here,  however,  we  see  the  application  of  the  categories 
with  which  we  have  become  familiar.  The  method 
assumes  that  there  are  at  least  some  cases  where  it  is  better 

178 


COMBINATIONS    AND    VARIATIONS  179 

to  require  the  student  to  observe  and  experiment  in  order 
to  learn  the  desired  fact,  rather  than  to  tell  him,  or  to  cite 
the  authority  of  a  writer.  Advocates  of  heuristic  methods 
maintain  also  that  it  is  fitting  that  we  require  the  discovery 
of  cause  and  effect  and  of  law  by  original  thinking,  at 
least  in  some  cases,  rather  than  to  give  them  by  authority, 
whether  this  authority  be  reenforced  by  efforts  at  verifi- 
cation on  the  part  of  the  student  or  not.  Here,  it  is  plain 
that  the  inductive  approach  may  be  utilized  to  discover 
cause  or  law,  but  it  is  equally  plain  that  deductive  use  may 
be  made  of  principles  or  causes  already  established,  in 
order  to  explain  what  has  occurred,  whether  in  the  affairs 
of  mice  or  men.1  It  has  already  been  shown  that  teaching 
as  an  art  must,  like  all  arts,  be  free  if  it  is  to  be  effective,2 
consequently  there  need  be  no  surprise  when  it  is  pointed 
out  that  all  writers  on  heuristic  methods  assume  that  the 
teacher  will  freely  use  all  the  means  at  his  disposal,  such 
as  observation,  experiment,  hypothesis,  analogy,  verifica- 
tion, invention,  and  the  like,  in  such  order  and  with  such 
emphasis  as  will  best  conserve  the  leading  purpose  of  the 
hour.  Induction  may  rule  for  a  day  or  a  week,  to  be 
preceded  or  succeeded  by  deduction;  or  deduction  may 
become  for  the  time  being  the  leading  process,  to  be  in  like 
manner  preceded  or  succeeded  by  induction;  or  the  two 
may  be  used  in  constant  reciprocal  interaction,  each  sup- 

1  See  exposition  in  Ch.  VL 
8  Compare  p.  83. 


l8o  SCIENTIFIC    METHOD    IN    INSTRUCTION 

plying  the  deficiencies  of  the  other,  and  both  serving  their 
turn  in  stimulating  the  mental  energies  of  the  student. 
The  skilful,  experienced  teacher  rarely  stops  to  ask  him- 
self which  step  in  a  thoroughly  scientific  method  comes 
next,  but  he  uses  instinctively  and  almost  automatically 
the  right  step  to  effect  the  result  desired;  or,  finding  no 
response  to  one  stimulus,  he  instantly  tries  another.  So 
the  mind  of  the  leader  and  the  minds  of  his  pupils  act 
and  interact,  often  with  great  rapidity  and  variety;  some- 
times with  slow,  earnest  labor,  step  by  step,  until  the  goal 
is  attained,  for  not  all  ideas  come  in  a  flash  or  can  develop 
in  a  minute. 

Good  teaching  needs  freedom  also  in  the  amount  of 
time  or  emphasis  that  is  to  be  devoted  to  the  various  as- 
pects of  the  subject  taught.  A  single  lesson  may  at  times 
(rare  in  the  experience  of  the  typical  school)  illustrate 
every  aspect  of  scientific  method,  and  thus  become  a 
show  piece  for  the  admiring  observer,  who  is  delighted 
to  see  in  a  nutshell  the  concentrated  essence  of  every 
method  known  to  man.  Usually,  however,  and  especially 
when  the  observer  is  not  present,  the  recitation  period  is 
devoted  more  to  some  one  phase  of  a  proper  method  than 
to  any  other,  or  perhaps  to  all  others  combined.  Welton  l 
happily  describes  these  varying  aspects  as  follows :  — 

"Though  every  form  of  the  learning  process  may  go  on 

1  James  Welton,  "  Principles  and  Methods  of  Teaching,"  pp.  72,  73, 
University  Pictorial  Press,  London, 


COMBINATIONS    AND    VARIATIONS  l8l 

in  any  one  lesson,  yet  a  little  reflection  makes  it  evident  that 
the  predominant  feature  in  one  differs  from  that  in  another. 
There  are  lessons  of  which  the  main  aim  is  the  increase 
of  information  or  the  apprehension  of  fact.  In  these  the 
learning  process  is  predominantly  perceptual.  There  are 
others  of  which  the  essential  purpose  is  to  examine  and 
analyze  facts  already  familiar,  so  as  to  reach  a  fuller 
understanding  of  them;  in  other  words  to  develop  theories 
and  general  ideas.  In  these  the  mental  process  in  learning 
is  essentially  conceptual,  and  the  order  of  thought  is  in- 
ductive. Thirdly,  there  are  those  whose  primary  function 
is  to  apply  and  utilize  knowledge  which  has  already  been 
acquired.  In  these,  also,  the  mental  process  of  learning 
is  conceptual,  but  the  order  of  thought  is  deductive.  And, 
fourthly,  there  are  lessons  which  tend  to  develop  con- 
structive and  executive  skill.  In  these  the  mental  process 
of  the  learner  is  either  imitative  or  imaginative,  and  in 
each  the  expression  of  the  ideas  by  some  form  of  physical 
activity  is  the  characteristic  feature." 

From  the  foregoing  it  can  be  seen  that  the  term  heuristic 
is  properly  used  to  describe  all  those  teaching  processes 
which  tend  to  awaken  and  stimulate  the  self-active  en- 
ergies of  the  student,  (i)  in  the  acquisition  of  facts, 
(2)  in  the  discovery  of  their  meaning,  and  (3)  in  gaining 
facility  in  their  intellectual  or  physical  application.  The 
term  enriches  our  methodological  vocabulary  to  the  extent 
that  in  teaching  it  implies  the  perfect  freedom  of  the 


1 82  SCIENTIFIC    METHOD    IN    INSTRUCTION 

teacher  to  use  any  or  all  means  available;  as,  for  example, 
any  form  of  approach,  whether  exclusively  inductive  or 
exclusively  deductive,  or  any  blending  of  the  two;  any 
kind  of  device,  already  known  or  freshly  invented,  to 
discover  facts  or  to  secure  results  in  construction.  Since 
the  teacher  not  only  has  this  freedom,  but  is  in  duty  bound 
to  exercise  it,  the  term  heuristic,  which  carries  this  impli- 
cation, is  a  good  one  to  use.1 

DISCUSSION  :  —  Proper  limits  for  the  heuristic  method  in 
the  several  studies. 

2.   Invention  as  a  Mode  of  Thought 

86.  Three  young  Germans  recently  set  themselves  the 
task  of  solving  this  problem :  How  transport  live  fish  from 
distant  rivers  to  Berlin  without  the  use  of  water-tanks? 
It  seems  the  people  of  that  city  are  willing  to  eat  salt- 
water fish  brought  in  dead  in  cold  storage,  but  are  unwilling 
to  use  fresh-water  fish  so  transported.  But  it  is  expensive 
to  carry  large  water-tanks  on  cars.  The  young  men  began 
the  analysis  of  this  problem  by  asking:  Why  must  fish 
have  water  to  keep  them  alive  ?  To  drink  ?  Not  probable. 
Evidently  to  carry  the  ah*  that  is  in  the  water  to  the  gills, 
that  they  may  absorb  the  oxygen  of  the  air  to  purify  the 
blood.  But  why  cannot  the  fish  get  the  needed  oxygen 
direct  from  the  air  without  the  aid  of  water?  Here  ex- 

1  The  author  who  writes  most  convincingly  on  this  subject,  especially 
for  elementary  teachers,  is  Henry  E.  Armstrong  in  "The  Teaching  of 
Scientific  Method,"  The  Macmillan  Co.,  N.Y. 


COMBINATIONS    AND    VARIATIONS  183 

perience  comes  to  their  aid.  Every  fisherman  knows  that 
fish  will  live  longer  out  of  water  in  the  shade  than  in  the 
sunshine;  in  dark,  damp  days,  than  in  bright,  dry  ones; 
furthermore,  that  if  water  be  dashed  over  them  occasion- 
ally life  may  be  greatly  prolonged.  What  then  seems  to 
be  the  immediate  cause  of  death  when  in  the  open  air? 
The  drying  out  of  the  gills  (and  doubtless  also  the  scales), 
for  so  long  as  they  remain  moist  the  fish  lives.  If  we  can 
devise  some  method  of  keeping  gills  and  scales  moist 
during  transportation,  will  the  fish  come  through  alive? 
Perhaps.  Let  us  assume  that  they  will. 

The  next  important  question  is,  What  causes  moist 
things  to  dry  out?  Evidently  the  presence  of  dry  or 
unsaturated  air;  for  so  long  as  the  atmosphere  is  not 
saturated  with  moisture  it  will  continue  to  absorb  it  from 
any  available  source.  How  can  any  moist  object  be  kept 
from  drying  out  ?  Evidently  by  keeping  it  in  a  saturated 
atmosphere.  But  how  shall  we  manage  to  do  this  with 
the  fish? 

It  is  certain  that  it  will  not  do  to  pack  them  in  barrels, 
even  if  covered  with  water,  for  the  mechanical  pressure 
would  prevent  the  gills  from  opening,  so  that  the  fish 
would  be  suffocated,  even  if  there  were  a  sufficient  supply 
of  oxygen  available.  "Let  us,"  said  one,  "take  a  tight 
dry-goods  box,  build  it  full  of  pigeon  (fish)  holes,  put  one 
fish  hi  each  compartment,  hang  up  wet  cloths  inside  to 
keep  the  air  saturated,  and  then  tightly  close  the  box." 


184  SCIENTIFIC    METHOD    IN    INSTRUCTION 

So  far,  so  good;  they  have  provided  for  permanent  mois- 
ture of  gills  and  scales,  and  have  made  suffocation  from 
pressure  impossible. 

A  new  query  now  arises:  How  shall  the  supply  of 
oxygen  be  renewed  without  introducing  the  outside  air, 
which  would  cause  the  gills  to  dry?  One  suggested  the 
introduction  of  saturated  air,  which  would  have  been 
satisfactory  except  for  the  trouble  of  preparing  it.  Finally, 
another  had  a  happy  thought,  — "  If  those  fish  need 
oxygen,  why  not  give  it  to  them?" 

Having  thought  their  problem  through,  they  made 
their  box  with  its  compartments,  enclosed  it  in  a  larger 
box  with  provision  for  saturating  the  air  inside,  con- 
nected a  bag  of  oxygen  with  the  interior  by  means  of 
a  glass  pipe,  arranged  for  a  small  vent  to  provide  for 
slow  ventilation,  caught  their  fish  and  put  them  drip- 
ping wet  inside,  nailed  the  whole  thing  up  tight,  and 
let  it  stand  for  four  days. 

Doubtless  they  held  many  animated  discussions  as  to 
the  correctness  of  their  reasoning  and  the  adequacy  of 
their  apparatus.  At  the  end  of  the  four  days,  however, 
they  opened  the  box  and  dumped  the  fish  into  a  pond. 
It  is  said  that  their  fish  distinguished  themselves  from  the 
other  fish  in  the  pond  by  the  vigor  of  their  motions  and  the 
keenness  of  their  hunger.  They  had  indeed  come  through 
alive,  but  they  were  empty,  and  tired  of  lying  still  while 
breathing  an  exhilarating  atmosphere. 


COMBINATIONS    AND    VARIATIONS  185 

Whether  the  experiment  actually  led  to  the  transporta- 
tion of  live  fish  from  distant  rivers  into  Berlin  or  not, 
the  exercise  was  a  good  one  in  inventive  thought.  The 
problem  was  analyzed  into  its  component  parts,  so  that 
the  difficulties  might  be  met  and  overcome  one  at  a  time, 
and  when  this  had  been  accomplished  the  whole  was  put 
to  the  test  of  trial.  Will  it  work?  This  is  the  process 
of  every  inventor,  whether,  like  Howe,  he  puts  the  eye  in 
the  wrong  end  of  the  needle,  and  thus  invents  the  sewing 
machine;  or  like  the  Massachusetts  man  who  has  recently 
invented  a  machine  for  separating  expeditiously  the  linen 
fibre  from  the  straw  of  flax,  thus  being  able  to  do  hi  an 
hour,  without  handling,  what  the  European  peasant  ef- 
fects only  as  the  result  of  much  handling  for  many  weeks. 
It  is  the  process  also  of  every  man  or  boy  who  meets  the 
exigencies  of  a  situation  in  new  ways.  A  lad  was  sent  to 
the  woods  with  a  team  for  a  load  of  rails.  They  were 
scattered  among  the  thick  undergrowth.  When  finally 
the  load  was  complete,  the  wagon  stuck  fast  on  a  sapling. 
Having  forgotten  to  take  an  axe  along,  the  lad,  with  hands 
in  pockets,  stood  hi  perplexity,  debating  which  would  cost 
the  less  labor,  to  go  for  the  axe  and  cut  down  the  sapling, 
or  to  unload  the  rails  and  perhaps  take  the  wagon  apart. 
Presently  he  noticed  that  the  sapling  was  almost  breaking 
with  the  strain  caused  by  the  pressure  upon  it,  and  his 
hand  being  upon  the  knife  in  his  pocket,  he  made  a  dart 
under  the  wagon,  caused  the  team  to  give  a  steady  pull, 


1 86  SCIENTIFIC    METHOD    IN    INSTRUCTION 

and  in  a  trice  had  the  sapling  cut  down  with  his  jack- 
knife. 

Such  inventive  thought  is  especially  the  prerogative 
of  the  laboratory  and  workshop,  where  apparatus  must  be 
devised  and  constructed,  and  where  all  the  inventive 
resources  of  the  youth  are  called  for  to  effect  desired  ends 
under  given  conditions.  It  is  the  wit  of  man  against  the 
fiat  of  circumstances;  it  is  what  enables  the  primitive 
man  and  the  pioneer  to  meet  the  requisites  for  survival; 
it  is  the  resource  of  those  who  must  make  a  little  go  a  long 
way  in  furnishing  the  necessities,  or  in  effecting  the  deco- 
rations of  the  home.  A  pleasant  distinction  is  to  be  made 
between  the  articles  thus  devised  by  the  bungler  on 
the  one  hand,  and  by  the  skilful,  inventive  thinker  on 
the  other.  The  latter  may  properly  call  attention  to  the 
difference  between  the  home-made  and  the  hand-made. 
The  element  of  inventive  thought  is  found  also  in  all 
original  work  in  drawing,  as  in  the  designing  of  articles 
or  of  their  decoration,  and,  as  every  artist  knows,  is  the 
very  life  and  heart  of  his  labor.  That  in  the  acquisition 
of  skill  in  the  arts  there  is  an  element  of  imitation  is  well 
known,  but  imitation  that  is  devoid  of  invention  soon 
reaches  its  limits  of  usefulness  as  an  educational  instru- 
ment.1 

DISCUSSION  :  —  Provision  that  can  be  made  for  inventive 
thought  in  the  respective  high-school  studies. 

1  Compare  Findlay,  "Principle  of  Class  Teaching,"  pp.  334-376. 


COMBINATIONS    AND    VARIATIONS  187 

3.  Analysis  and  Synthesis 

87.  Not  a  little  confusion  has  at  times  been  occasioned 
in  methodology  by  attempts  to  regard  analysis  and  syn- 
thesis as  complete  methods,  and  in  trying  to  identify 
them  with,  or  distinguish  them  from,  induction  and  de- 
duction respectively.  The  confusion  arises  from  two 
circumstances ;  namely,  first,  that  the  purpose  of  an  analy- 
sis may  not  be  that  of  induction  at  all,  or  the  purpose  of 
a  synthesis  that  of  deduction;  and  second,  that  the  kind 
of  things  which  may  be  analyzed  into  elements,  or  the  kind 
of  elements  that  may  be  united  into  wholes,  is  virtually 
unlimited.  We  may  analyze  anything,  and  do  so  when 
we  separate  it  into  its  elements,  for  any  purpose  what- 
soever; and  we  may  synthesize  any  elements  that  we  can 
contrive  to  get  together,  again  for  any  conceivable  purpose. 
We  may  analyze  a  word  into  elements  to  see  how  it  is 
spelled;  a  constructive  problem,  to  meet  and  overcome 
its  difficulties  one  by  one,  as,  for  instance,  hi  the  problem 
of  the  transportation  of  live  fish  above  described;  a  politi- 
cal situation,  in  order  to  know  how  to  vote;  and  so  on 
throughout  the  manifold  affairs  of  life.  A  conception  has 
both  content  and  extent;  either  may  be  analyzed;  a 
fact  may  have  both  essential  or  significant  aspects,  as  in 
detective  work,  and  insignificant  ones;  analysis  enables 
us  to  separate  the  one  from  the  other.  A  mathematical 
problem  may  be  analyzed  in  order  to  lead  to  its  solution. 


1 88  SCIENTIFIC    METHOD    IN    INSTRUCTION 

We  may  analyze  experience  to  find  the  factors  that  will  be 
useful  to  us  upon  any  given  occasion,  or  under  any  given 
circumstances.  There  is  mathematical  analysis,  and 
chemical  analysis,  and  logical  analysis,  and  critical  analy- 
sis, and  psychological  analysis;  there  is  analysis  in  arts 
and  sciences  and  in  practical  affairs,  —  there  are,  in  short, 
as  many  kinds  and  methods  of  analysis  as  there  are 
different  wholes  to  be  resolved  into  elements.  The  con- 
verse of  all  this  is  equally  true  for  synthesis.  We  even 
read  of  the  Pollard  synthetic  method  of  teaching  reading 
to  children. 

Manifestly,  only  confusion  can  arise  from  any  attempt 
to  identify  analysis  with  induction,  for  there  are  many 
methods  of  analysis  and  many  purposes  for  which  it  is 
made,  but  there  is  but  one  method  and  one  purpose  for 
induction;  the  method,  namely,  of  inferring  the  general 
from  the  particular,  and  the  purpose  of  arriving  at  a  gen- 
eralization of  some  sort. 

The  better  way  is  to  regard  analysis  simply  as  a  mani- 
foldly varied  means  of  separating  aggregates  into  their 
elements,  be  the  purpose  of  the  separation  what  it  will; 
and  conversely,  of  regarding  synthesis  as  an  equally  varied 
means  of  uniting  elements  into  aggregates,  let  the  purpose 
of  the  union  be  what  it  may. 

DISCUSSION  :  —  Distinguish    between    mathematical    and 
chemical  analysis;  between  psychological  and  critical  analysis. 


COMBINATIONS    AND    VARIATIONS  189 

4.   Some  German  Methods 

88.  German  writers  l  on  methods  of  teaching  usually 
distinguish  at  least  three  distinct  aspects  to  a  scientific 
method,  as  follows:  — 

1.  The  telling,  or  lecture  aspect. 

2.  The  expository  aspect. 

3.  The  development  aspect. 

The  telling,  or  lecture  method,  serves  for  imparting 
facts  on  the  authority  of  the  teacher,  while  exposition  and 
development  serve  to  enable  the  student  to  comprehend  the 
significance  of  the  facts  thus  imparted;  that  is,  to  discover 
and  understand  causes,  effect  classifications,  and  derive 
generalizations,  partly  at  least  through  the  student's  own 
thinking. 

The  American  high-school  teacher,  fresh  from  the 
university,  is  often  reproved  for  his  proneness  to  fall  into 
the  lecture  type  of  instruction,  but  to  the  German  teacher 
this  is  the  standard  method  of  imparting  information.  All 
his  life  he  has  learned  in  this  way,  and  it  hardly  occurs  to 
him  that  there  is  any  other.  From  the  time  he  enters  the 
elementary  school  at  six,  until  he  leaves  for  the  university, 
his  teachers  have  in  general  spent  about  half  of  each  period 
of  fifty  or  fifty-five  minutes  in  telling  him  facts,  and  the 
other  half  of  the  hour  in  calling  for  their  repetition  and 

1  Compare  Willmann,  "Didaktik  als  Bildungslehre,"  Vol.  II,  pp.  380- 
453- 


190  SCIENTIFIC    METHOD    IN    INSTRUCTION 

explanation.  The  same  method  is  followed  in  the  univer- 
sity, with  the  exception  that  the  lecturer  now  spends  the 
entire  period  with  his  lecture,  leaving  review  to  the  stu- 
dent's note-book,  and  understanding  to  his  private  reflec- 
tion. Consequently,  to  the  German,  telling  becomes  the 
most  natural  method  of  teaching. 

A  considerable  part  of  training  for  teaching  in  Germany 
is  devoted  to  the  theory  and  practice  of  narration,  as  the 
chief  means  for  imparting  information  to  the  students. 
The  candidate  is  taught  to  utilize  freely  the  principle  of 
apperception  in  introducing  his  lesson;  to  use  the  heuristic 
method  of  arousing  interest  in  what  is  to  be  given,  by 
inducing  reflection  on  related  matters;  and  to  employ 
direct  sense  perception,  or  observation,  by  the  pupils, 
whenever  this  is  possible.  Pictures,  maps,  and  objects  are 
to  be  freely  used  whenever  suitable  and  available.  The 
lesson  itself  must  be  presented  in  simple,  forceful  language, 
with  good  diction  and  animated  delivery.  It  must,  when 
possible,  as  in  history,  assume  the  narrative  form,  with 
the  classic  epic  as  a  model.  Be  as  good  a  story-teller  as 
Homer  and  you  will  be  sure  to  have  the  interested  attention 
of  the  pupils,  the  trainer  admonishes.  Make  the  story 
vivid,  throw  a  strong  light  on  the  leading  actors  and  events, 
arrange  all  in  due  order,  bring  to  bear  every  resource  of 
literary  art,  so  that  it  will  be  more  easy  and  natural  to 
remember  than  to  forget.  Who  that  has  once  read  and 
experienced  in  imagination  the  adventures  of  Ulysses 


COMBINATIONS    AND    VARIATIONS  191 

ever  loses  any  essential  part  of  that  immortal  tale  ?  Learn 
of  the  ancient  rhetoricians,  who  emphasized  five  points 
for  the  orator:  — 

1.  The  getting  of  the  material,  —  invention. 

2.  The  arrangement  of  the  material,  —  disposition. 

3.  The  diction  to  be  chosen,  —  elocution. 

4.  Impression  that  will  surely  lead  to  recall,  —  memory. 

5.  The  speech  itself,  —  action. 

Then,  after  all  this  has  been  done,  learn  to  pass  easily 
from  monologue  to  dialogue,  to  that  review  and  elaboration 
that  secure  retention  and  understanding. 

American  secondary  schools  are  not  so  organized  that 
this  method  can  be  successfully  used  in  them.  In  the 
first  place,  our  periods  for  recitation  are  much  shorter 
than  the  German,  so  that  they  cannot  readily  be  divided 
somewhat  equally  between  narration  by  the  teacher  and 
reproduction  by  the  students.  In  the  second  place, 
American  teachers  rely  upon  the  text-books  for  the  facts 
to  be  mastered  by  the  student,  whereas  Germans  expect 
the  teacher  to  carry  in  his  head  and  properly  arrange  all 
that  is  to  be  imparted.  Then,  American  students  have 
study  periods  at  school,  whereas  German  students  do  not, 
since  practically  all  school  hours  are  with  them  recitation 
hours.  As  a  natural  consequence  of  these  conditions, 
any  effort  of  the  beginner  in  the  American  high  school 
to  ignore  the  text-book  as  a  source  of  facts,  and  the  study 
hour  as  a  time  for  learning  them,  is  sure  to  be  looked  upon 


IQ2  SCIENTIFIC    METHOD    IN    INSTRUCTION 

as  an  unwise  innovation,  and  reproved  accordingly. 
What  makes  it  worse  for  the  would-be  lecturer  is  that  the 
periods  are  too  short  to  secure  the  requisite  time  for  the 
preparation  and  elaboration  and  review  that  are  neces- 
sary for  the  successful  utilization  of  this  primitive  method, 
inherited  from  Greeks,  but  perfected  by  Germans. 

DISCUSSION  :  —  Relative  usefulness  of  the  lecture  method 
in  the  various  subjects  under  American  conditions. 

89.  The  expository  method  is  concerned  with  the  ex- 
planation of  facts  already  imparted,  and  falls  into  two 
main  divisions,  —  the  exposition  of  difficult  points   (i) 
of  language,  and  (2)  of  things  and  events.    The  diffi- 
culties of  language  find  their  exposition  chiefly  in  con- 
nection with  translation,  whereas  those  that  relate  to 
natural  phenomena  or  to  historical  events  are  treated  in 
the  laboratory  or  in  the  regular  recitation.    The  various 
stages  of  such  work  in  Latin  have  already  been  indicated 
in  Section  73.    The  exposition  of  difficult  points  in  the 
comprehension  of  events  in  the  natural  or  in  the  historical 
world  is  made  chiefly  by  the  aid  of  the  deductive  applica- 
tion of  known  principles,  as  already  sufficiently  explained 
in  the  chapter  on  The  Deductive  Approach. 

90.  The  third,  or  development  method,  is  precisely  that 
of  the  American  school,  and  may  be  (i)  of  the  inductive 
type,  where  authority,  observation,  and  experiment  give 
the  facts,  and  hypothesis,  analogy,  and  inductive  inference 


COMBINATIONS    AND    VARIATIONS  193 

suggest  the  law,  while  deductive  verification  confirms  or 
rejects  it;  and  (2)  of  the  deductive  type,  either  in  antici- 
pation of  what  is  or  will  be  true,  or  for  the  purpose  of  gain- 
ing new  knowledge  and  insight  respecting  facts  and  laws. 

91.  From  every  point  of  view,  therefore,  there  is  con- 
vincing confirmation  of  the  fact  that  the  essential  elements 
of  all  rational  methods  are  few  hi  number  and  easy  to 
understand,  however  difficult  they  may  be  to  apply  wisely 
and  well.  They  are  employed  by  the  scholar  in  his  study, 
the  scientific  man  in  his  laboratory,  the  inventor  hi  his 
workshop,  the  merchant  hi  his  counting-house,  the  manu- 
facturer in  his  office,  the  statesman  in  the  halls  of  legisla- 
tion. Every  man,  in  short,  who  deals  with  facts  and  their 
significance,  must  perforce  use  the  categories,  and  follow 
the  order  of  thought  described  hi  this  work,  if  he  would  be 
master  of  his  problem,  and  control  his  situation.  The 
school  is  the  place  where  men  should  learn  to  do  their 
work,  —  to  gather  facts,  to  think  out  their  meaning,  and 
to  become  effective  in  their  utilization.  That  the  teacher 
may  see  more  clearly  than  he  perhaps  saw  before  what 
these  essential  elements  are,  and  that  he  may  do  his  work, 
at  first  with  deeper  insight,  and  eventually  with  greater 
skill  than  before,  the  foregoing  exposition  has  been  written. 
The  sources  from  which  the  facts  and  arguments  of  this 
volume  have  been  drawn  are  open  and  commended  to 
all. 

o 


INDEX 


Acquiring  the  facts  for  an  induction, 

85- 

Acquisition  of  facts,  3. 
Adolphus,  Gustavus,  4. 
Agreement  and  difference,  the  joint 

method  of,  51. 
Agreement  or  difference,  method  of, 

43- 

Agreement,  the  method  of,  48. 

Alexander  the  Great,  soldiers  of,  13. 

"All  is  in  all,"  Jacotot,  165. 

Aluminum,  125. 

Amount  of  knowledge  to  be  acquired 
by  student,  69. 

Amphioxus,  class  of,  21. 

Analogy,  as  a  guide  to  discovery,  41 ; 
hypothesis  and,  28. 

Analysis  and  synthesis,  187. 

Andrews,  E.  P.,  restoration  of  in- 
scription on  Parthenon,  22. 

Anopheles,  40. 

Anteroom  and  vestibule,  158. 

Anticipation,  deductive,  124;  in  litera- 
ture, 127. 

Apperception,  bias  of,  7;  inductive 
processes  of,  79;  processes  of 
deduction,  123. 

Application,  in  mathematics,  1 73 ;  pro- 
cesses of,  150. 

Approach,  the  deductive,  122. 

Argon,  discovery  of,  9. 

Aristotle,  authority  of,  6;  founda- 
tions of  zoology,  12. 

Armstrong,  Henry  E.,  91,  107,  182. 

Artificial  observation,  14. 

Ascham,  164. 

Authority,  3. 

Bacon,  Edwin  M.,  96. 

Bacon,  Francis,  an  authority,  6;  new 

method  of,  76. 
Bagley,     W.    C.,    "The    Educative 

Process,"  124. 
Bain,  50,  54,  55.  «7»  98- 


Baker,  Scott,  and  Carpenter  on  Eng« 
lish,  84. 

Bancroft,  89. 

Barnes,  Mary  Sheldon,  91,  95. 

Barometer,  problem  of,  85. 

Battle  of  Shiloh,  John  Fiske  on,  24. 

Because,  deductive  force  of,  122. 

Bees,  Huber's  experiment  on,  35. 

Bennett  and  Bristol  on  "The  Teach- 
ing of  Latin  and  Greek,"  84. 

Bennett,  Charles  E.,  161,  163. 

Bequest  to  Swarthmore  College,  126. 

Bergen's  "Elements  of  Botany,"  90. 

Bessemer  process,  27. 

Bias  of  apperception,  7. 

Biology,  inductive  approach  to,  107. 

Bourne,  Henry  E.,  "The  Teaching  of 
History  and  Civics,"  84. 

"Bring  the  factory  to  the  farm,"  81. 

"  Bring  the  farm  to  the  factory,"  81. 

Bristol,  George  P.,  161. 

Buck,  169. 

Buckle's  "  History  of  Civilization,"  44. 

Burke,  quoted,  28. 

Canada,  no  heretics  in,  146. 
Carpenter,  Baker,  and  Scott,  84,  119. 
Cathedral,  St.  Paul's,  14. 
Cauer's  Die  Kunst  des    Uebersetzens, 

161. 

Cause  and  effect,  94. 
Cause  of  rust,  28. 
Causes,  determination  of,  43. 
Cavendish,  9. 
Chamberlain,    Joseph    E.,    "Ifs    of 

History,"  127. 

Changa,  or  the  mole  cricket,  85. 
Charles  I  of  England,  113,  127. 
Chemistry  and  physics,  Smith  and 

Hall  on,  84. 
Chemistry,    inductive    approach    to, 

106. 
Chubb,  Percival,  on  "The  Teaching 

of  English,"  84,  169. 


'95 


196 


INDEX 


Civics  and  history,  Henry  E.  Bourne 

on,  84. 
"Civil  War  in  the  Mississippi  Valley, 

The,"  81. 

Classification,  55,  96. 
Class,  the,  in  observation,  10. 
Clerk-Maxwell's     analogy     between 

water  and  electricity,  41. 
Collar,  164. 

Collective  experiments,  20. 
Colton,  quoted  on  classification,  58. 
Comenius,  a  new  method  for  teaching 

Latin,  91. 
Committee   of  Ten,    Report   of,   on 

concrete  geometry,  no. 
Complacency,  dogmatic,  133. 
Composition  in  English,  166. 
Concomitant   variations,  method   of, 

52- 

Concrete  geometry,  no. 
Conditions,  similarity  of,  19. 
Control  of  the  variable,  15. 
Cooperation  in  composition,  166. 
Corson,    Hiram,    "The    Voice    and 

Spiritual  Education,"  145. 
Cotton-gin,  87. 
Courts,  3. 
Cramer,    Frank,    "The    Method    of 

Darwin,"  91. 
Creighton,  J.  E.,  51. 
Culex  stegomyia,  40. 
Culture,  definition  of,  vi. 
Czar  of  Russia,  127. 

Daniell,  164. 

Darwin,  8,  128. 

Death's-head  moth,  n. 

Deduction,  function  of,  in  gaining  new 
knowledge,  129;  in  natural  sciences, 
147;  in  nature  study,  130;  in  school 
vs.  deduction  in  science,  76. 

Deductive  approach,  the,  122. 

Deductive  nature  of  linguistics,  140. 

"Degree,  the  third,"  4. 

Dementia,  telling,  89. 

DeMorgan,  108,  134,  173. 

Descartes  on  algebra  and  geometry,  41 . 

Determination  of  causes,  43. 

Deulsches  Lesebuch,  72. 

Development  method  in  German 
schools,  192. 


Dewey,  154. 

Difference,  the  method  of,  50. 
Discipline,  definition  of,  vi. 
Discovery  of  Neptune,  54. 
Dissection,  plant,  89. 
Dogmatic  complacency,  133. 
Dowden,  Professor,  119. 
Droysen,  Professor,  24. 
Drude,  Paul,  37. 

Earthworms,  effect  on  soil,  8. 
Educational    status    of    high-school 

students,  67. 

Education  a  preparation  for  life,  157. 
Efficiency,  need  of,  73. 
English :  Carpenter,  Baker,  and  Scott 

on,  84 ;  composition  in,  1 66 ;    Perci- 

val  Chubb  on,  84. 
Epic,  the,  as  model,  190. 
Essential     aspects     of     geometrical 

problems,  139. 
Evidence,  rules  of,  46. 
Experiment,  14. 
Experiments,  collective,  20. 
Experimentum  cruets,  the,  37. 
Explanation,  means  of,  28. 
Exposition  in  German  schools,  192. 

Factory,  bring  the  farm  to  the,  81. 

Facts,  acquisition  of,  3. 

Facts,  for  induction,  how  acquired,  87 ; 
meaning  of,  explanation  of,  21. 

'  Fall  line,'  the,  82. 

Farm,  bring  the  factory  to  the,  81. 

Field  of  knowledge,  location  of  stu- 
dent in,  68. 

Findlay,  186. 

Fjrst  requisite  for  a  good  hypothesis, 

32- 

Fish,  transportation  of,  182. 
Fiske,  John,  text-book  vs.  treatise  on 

history,  81. 

Foreign  languages,  induction  in,  113. 
'Formal  steps,'  75. 
Forms,  of  application,  155 ;  of  solution 

for  the  problem,  43. 
Francis  Bacon  on  authority,  6. 
Francis  Parkman,  cause  of  thunder, 

3i- 

French  Revolution,  113. 
Froebel,  154. 


INDEX 


107 


Frontier,  significance  of,  80. 
Function  of  deduction,  129. 
Functions  of  the  laboratory,  169. 

Galileo,  invention  of  telescope,  22 ;  on 
velocity  of  b'ght,  16. 

Generalization,  60;  nature  and  func- 
tions of,  99. 

Generalizations,  mathematical,  63 ; 
non-mathematical,  60. 

Geometrical  hypothesis,  30. 

Geometrical  problems,  essential  as- 
pects of,  139. 

Geometry,  concrete,  no;  plans  for 
teaching,  138. 

German  methods,  some,  189. 

German  theories  of  language  teach- 
ing, 115. 

Goats  as  disease  bearers,  46. 

Golden  Rule  of  classification,  57. 

Goldwin  Smith,  89. 

Grammar,  the  teaching  of  English, 
118. 

Grant,  146. 

Greek  and  Latin,  Bennett  and  Bristol 
on,  84. 

Gustavus  Adolphus,  4. 

Haeckel,  154. 

Hall  and   Smith,  on  chemistry  and 

physics,  84. 

Hall,  Edwin  H.,  133,  154. 
Hamlet,  22,  128. 
Harris,  W.  T.,  12,  123,  154. 
Hart,  Albert  Bushnell,  96. 
Havana  experiments  on  yellow  fever, 

38- 
Henry,   Patrick,   on  use    of  history, 

126. 

Herbart,  154. 
Herbartians,     German,    on    'formal 

steps,'  75. 

Heretics  in  Canada,  no,  146. 
Heuristic  method,  the,  178. 
Hinsdale,  B.  A.,  95. 
Historians,  4. 
History  and  civics,  Henry  E.  Bourne 

on,  84. 

"History,  Ifs  of,"  Chamberlain,  127. 
History,  induction  in,  112;  text-books 

in.  79- 


"History  of  Civilization,"   Buckle's 

44- 

Hoadley,  George  A.,  103. 
Home-made  vs.  hand-made,  186. 
Hooke,  14. 
Howe,  185. 

Huber,  experiment  on  bees,  35. 
Huxley  on  observation,  7,  8,  56,  154. 
Hypothesis  and  analogy,  28. 
Hypothesis,  geometrical,  30 ;  meaning 

and  use  of,   28;    requisites  for  a 

good,    32,    33,    34;    the,   93;    the 

Ptolemaic,  31 

"Ifs  of  History,"  Chamberlain,  127. 

Induction,  immediate  purpose  of,  77; 
in  foreign  languages,  113;  in  his- 
tory, 112. 

Inductions,  mathematical,  87. 

Inductive  approach,  the,  75. 

Inductive  approach  to  thought  pro- 
cesses, 91. 

Insanity,  Hamlet's,  22. 

Instruction,  scientific  method  in,  64- 
190. 

Invention,  as  a  mode  of  thought,  182; 
as  problem  solving,  23;  of  tele- 
scope, Galileo,  22. 

Jacotot's  "Universal  Method,"  118, 
165. 

Jena,  battle-field  of,  10. 

Jevons,  William  Stanley,  28,  33,  36, 
37,  42,  62. 

John  Fiske,  31,  44,  89,  146,  241. 

John  Locke,  stones  growing,  34. 

Joint  method  of  agreement  and  differ- 
ence, 51. 

Joule,  James  Prescott,  19. 

Jupiter,  moon,  velocity  of  light,  17. 

Kant  paraphrased,  73. 
Knowledge,  amount  of,  to  be  acquired, 
69. 

Laboratory,  functions  of  the,  148, 
169;  shop,  workroom,  158;  in 
English  composition,  167. 

Laboratory  method  in  mathematics, 

175- 
Lancelet,  the,  Colton  on,  59. 


198 


INDEX 


Latin  and  Greek,  Bennett  and  Bristol 

on,  84. 

Latin  grammar,  163. 
Lazear,  Dr.,  38. 
Lecture  method,  the,  189. 
Lessing,  quoted,  28. 
Lester  F.  Wood,  42. 
Life,  education  a  preparation  for,  157. 
Light,  experiments  on,  100;    velocity 

of,  Romer,  17. 

Linguistics,  deductive  nature  of,  140. 
Locke,  John,  stones,  34. 
Logic  of  sense  perception,  Harris,  12. 
Loomis,  Elisha  S.,  140. 
Lord  Rayleigh,  argon,  8. 
Louis  XIV  and  heretics,  146. 
Louis  XVI  of  France,  127. 
Liitzen,  battle  of,  4. 

McCormick  reaping  machine,  26. 

McMaster,  89. 

McMurry,  Charles  A.,  73. 

Macbeth,  87. 

Mach,  Ernst,  18,  21,  31. 

Mackenzie,  cited,  42. 

Mahy,  M.  Catherine,  168. 

Malta,  English  soldiers  at,  46. 

Malthusian  law  of  population,  34. 

Mammoths  in  Siberia,  Mach  on,  31. 

Mathematical  generalizations,  63. 

Mathematical  inductions,  87. 

Mathematics,  application  in,  173; 
David  Eugene  Smith  on,  84;  de- 
ductive nature  of,  137;  induction 
in,  108;  J.  W.  A.  Young  on,  84. 

Meaning  and  use  of  hypothesis,  28. 

Meaning  of  facts,  21. 

Means  of  explanation,  28. 

Mediatory  office  of  Portia,  90. 

Method,  heuristic,  178;  in  instruc- 
tion, 64-190;  of  agreement  or  dif- 
ference, 43;  of  agreement,  the,  48; 
of  concomitant  variations,  52. 

"  Method  of  Darwin,  The,"  by  Frank 
Cramer,  91. 

Method,  of  difference,  the,  50;  of 
residues,  53;  the  lecture,  189. 

Methods,  some  German,  189. 

Mill's  five  rules  of  evidence,  47. 

Mole  cricket,  the,  85. 

Moore,  175. 


Mosquito,  the,  in  yellow  fever,  38. 
Moth,  death's-head,  n. 
Motion,  perpetual,  33. 
Motley,  89. 
Muff,  Dr.  Charles,  72. 
Munch,  Wilhelm,  160. 
Miinsterberg,  3. 
Myers,  175. 

Natural  sciences,  deduction  in,  148. 
Nature  study  vs.  high-school  science, 

131- 

Neptune,  discovery  of,  54. 

New  method,  the,  of  Bacon,  76. 

New  movement  among  physics  teach- 
ers, 104. 

Nodes  of  thought  in  studies,  70. 

Non-mathematical  generalizations,  60. 

Observation,  6,  9,  10,  14. 

Olaf  Romer,  velocity  of  light,  17. 

Parkman,  89. 

Parthenon,  restoration  of  inscription, 
22. 

Patrick  Henry  on  uses  of  history,  126. 

Patten,  Simon  N.,  34,  41,  44. 

Payne's  "Lectures  on  Education," 
118,  165. 

Pearson,  Karl,  154. 

Perpetual  motion,  33. 

Perry,  John,  175. 

Pestalozzi,  154. 

Physics,  German  and  French  associa- 
tions on,  104. 

Plant  dissection,  89. 

Portia,  mediatory  office  of,  90. 

Porto  Rico,  the  changa,  or  mole 
cricket,  85. 

Priestley  on  hypotheses,  30. 

Problem,  forms  of  solution  of,  43; 
setting  the,  82;  the,  21;  the,  in 
induction,  79;  the,  universality  of, 

23- 
Problems,   magnitude  of,   24;    serial 

arrangement  of,  26. 
Proceedings  of  the  Royal  Society,  8. 
Processes  of  apperception,  inductive, 

78;  deduction,  123. 
Processes   of    application,    induction 

and  deduction,  150. 


INDEX 


199 


Processes  of  thought,  deduction,  129; 

inductive  approach,  91. 
Proneness  to  deduction,  the  teacher's, 

129. 

Psychologist  vs.  sociologist,  152. 
Ptolemaic  hypothesis,  31. 
Purpose  of  induction,  77. 

Railroad,  principal  inventions  for,  27. 
Ramsay,  William,  argon,  8. 
Rayleigh,  Lord,  argon,  8. 
Recapitulation   of   race   acquisitions, 

69. 

Red  Water  on  cause  of  thunder,  31. 
Report  of  the  Committee  of  Ten  on 

concrete  geometry,  no. 
Requisite,  first,  for  a  good  hypothesis, 

32;   second,  for  a  good  hypothesis, 

33;    third,  for  a  good  hypothesis, 

34- 

Residues,  method  of,  53. 
Roger  Bacon  on  generalizations,  61. 
Romaines,  George  John,  35. 
Romer,  Olaf,  velocity  of  light,  17. 
Royal  Society,  Proceedings  of,  8. 
Rules  of  evidence,  46. 
Rupert,  William  W.,  140. 
Russell,  "  German  Higher  Schools," 

114,  115,  117. 
Russia,  the  Czar  of,  127. 
Rust,  cause  of,  28. 
Ruth,  sickle  of,  26. 

Sapling,  cutting  the,  185. 

Schemer  vs.  his  scheme,  the,  117. 

Scientific  method  in  instruction,  64- 
190. 

Scientific  method,  stages  of,  78. 

Scott,  Carpenter,  Baker  and,  on 
English,  84. 

Second  requisite  for  a  good  hypothe- 
sis, 33- 

Setting  the  problem,  82. 

Shakespeare,  treatment  of  super- 
natural by,  90. 

Sherman  on  pursuit  at  Shiloh,  25. 

Shop,  laboratory,  workroom,  158. 

Sickle,  Ruth's,  26. 

Significance  of  the  frontier,  80. 

Similarity  of  conditions,  19. 

Skeleton,  the  thoughts  of  a,  132. 


Smith  and  Hall,  "The  Teaching  of 
Chemistry  and  Physics,"  84,  133. 

Smith,  David  Eugene,  "The  Teach- 
ing of  Elementary  Mathematics," 
84. 

Smith,  Goldwin,  89. 

Sociologist  vs.  psychologist,  152. 

Solution,  forms  of,  for  problem,  43. 

Some  German  methods,  189. 

Spencer,  42,  154. 

Stages,  of  observation,  10 ;  of  scientific 
method,  78. 

Status  of  high-school  students,  edu- 
cational, 67. 

Stones  growing,  Locke,  34. 

St.  Paul's  Cathedral,  14. 

Supernatural,  treatment  of,  in  Shake- 
speare, 90. 

Swarthmore  College  bequest,  126. 

Synthesis  and  analysis,  187. 

Teaching  a  free  art,  83. 
Teaching  vs.  telling,  68. 
Telescope,  invention  of,  by  Galileo, 

22. 

Telling  dementia,  89. 
Telling  vs.  teaching,  68. 
Text-books  in  history,  79. 
"The    Educative    Process,"   Bagley, 

124. 

Thermite,  125. 
"  The  third  degree,"  4. 
Thirty  Years'  War,  24. 
Thought,  processes  of — induction,  91. 
Tolman,  Herbert  Gushing,  161. 
Torrey,  Joseph,  Jr.,  106. 
Translation  as  application,  159. 
Transportation  of  live  fish,  182. 
Turner  on  "The  Significance  of  the 

Frontier  in  American  History,"  80. 
Type,  the,  as  basis  of  classification, 

57- 
Types,  function  and  value  of,  70;  in 

English,  72 ;  in  geography,  73. 
Tytler,  Alex.  Fraser,  160. 

"  Universal  instruction,"  Jacotot,  165. 

Vanillin  as  plant  poison,  53. 
Variable,  the,  control  of,  15. 
Variant,  the,  15. 


2OO 


INDEX 


Velocity  of  light,  Galileo,  Romer,  17. 
Vestibule  and  anteroom,  158. 
Vicariousness,  no  place  in  education, 

v. 
Victor,  essay  on  language  teaching, 

114. 
Von  Holtz,  89. 

Wallace,  cited,  42. 

Ward,  Lester  F.,  cited,  43. 

Watt,  8. 


Welton,  James,  180. 
Willmann,  O.,  143,  189. 
Workroom,  laboratory,  shop,  158. 

Yellow   fever,    Havana   experiments, 

38- 

Y.M.C.A.  and  physics,  170. 
Young,  J.  W.  A.,  "The  Teaching  of 

Mathematics,"  84,  175,  177. 

Zoology,  Aristotle  founder  of,  12. 


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DYNAMIC  FACTORS  IN  EDUCATION 

By  M.  V.  O'SHEA,  Professor  of  the  Science  and  Art  of  Education, 
sity  of  Wisconsin.     Cloth.     I2mo.     xiii  +  320  pages.     $1.25 

This  volume  is  the  result  of  the  author's  conviction  that  the  motor 
and  physical  factors  should  receive  more  attention  than  they  now  do 
in  most  cases.  In  the  first  part  he  shows  that  in  the  early  years,  at 
any  rate,  motor  expression  is  essential  to  all  learning,  and  he  has 
indicated  how  the  requirements  of  dynamic  education  can  be  pro- 
vided for  in  all  departments  of  school  work.  Attention  is  paid  also 
to  the  definite  order  in  which  the  motor  powers  develop.  The 
second  part  of  the  book  treats  the  relation  between  fatigue  and 
activity.  On  the  one  side  the  nature  and  causes  of  fatigue  are  dis- 
cussed and  then  the  effects  upon  mind  and  body  are  traced.  Much 
space  is  given  to  pointing  out  ways  and  means  of  carrying  on  the 
work  of  the  schoolroom  without  overtaxing  the  pupil.  Dr.  O'Shea 
has  summarized  the  investigations  made  upon  the  different  topics 
discussed  by  specialists  and  has  added  his  own  observations  made 
upon  children  whose  development  he  has  followed  in  detail  for  a 
number  of  years.  Topics  for  investigation  and  discussion  designed 
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LINGUISTIC  DEVELOPMENT  AND  EDUCATION 

By  M.  V.  O'SHEA.     I2mo.     Cloth,    xvii+347  pages.     $1.25 

A  study  of  the  psychology  of  linguistic  development  derived  from 
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has  been  acquired.  The  history  and  methods  of  these  observations, 
and  the  deductions  made  in  reference  to  linguistic  functions,  form 
the  substance  of  a  volume  which  will  have  great  interest  for  all 
students  both  of  language  and  of  mental  development 


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THE   PHILOSOPHY   OF   EDUCATION 

By  HERMAN  HARRELL  HORNE,  Assistant  Professor  of  Philosophy  and 
Pedagogy  in  Dartmouth  College.  8vo.  Cloth,  xvii  +  295  pages. 
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A  connected  series  of  discussions  on  the  foundations  of  educa- 
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philosophy,  and  a  thoroughgoing  interpretation  of  the  nature,  place, 
and  meaning  of  education  in  our  world.  The  newest  points  of  view 
in  the  realms  of  natural  and  mental  science  are  applied  to  the  under- 
standing of  educational  problems.  The  field  of  education  is  care- 
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THE  PSYCHOLOGICAL  PRINCIPLES  OF 
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By   HERMAN   HARRELL   HORNE.      Cloth.      12010.      xiii  +  435  pages. 

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The  relationship  of  this  book  to  the  author's  "Philosophy  of 
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practice,  this  is  mostly  practice  with  some  theory.  This  volume 
lays  the  scientific  foundations  for  the  art  of  teaching  so  far  as  those 
foundations  are  concerned  with  psychology.  The  author  is  the 
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the  theoretical  descriptions  of  pure  psychology  and  transforming 
them  into  educational  principles  for  the  teacher.  In  the  Introduc- 
tion the  reader  gets  his  bearings  in  the  field  of  the  science  of  educa- 
tion. The  remainder  of  the  book  sketches  this  science  from  the 
standpoint  of  psychology,  the  four  parts  of  the  work,  Intellectual 
Education,  Emotional  Education,  Moral  Education,  and  Religious 
Education,  being  suggested  by  the  nature  of  man,  the  subject  of 
education.  A  special  feature  is  the  attention  paid  to  the  education 
of  the  emotions  and  of  the  will. 


THE   MACMILLAN   COMPANY 

64-66  FIFTH  AVENUE,  NEW  YORK 

a 


METHODS   IN  TEACHING 

Being  the  Stockton  Methods  in  Elementary  Schools.  By  Mrs.  ROSA 
V.  WINTERBURN,  of  Los  Angeles,  and  JAMES  A.  BARR,  Superin- 
tendent of  Schools  at  Stockton,  Cal.  i2mo.  Cloth,  xii  +  355  pages. 
$1.25 

This  book  is  a  direct  product  of  the  schoolroom.  It  treats  the 
presentation  of  subject-matter  in  the  various  studies  usually  taught 
in  elementary  schools  from  three  points  of  view  —  that  of  the  super- 
intendent or  supervisor,  of  the  teacher,  and  of  the  pupil.  The  book 
grew  out  of  the  exhibit  made  by  the  Stockton  schools  at  the  Expo- 
sition in  St.  Louis,  and  later  in  Portland,  which  attracted  widespread 
attention  because  of  the  honesty  of  the  pupils'  work,  the  "  method 
sheets  "  by  teachers,  and  the  efficiency  of  results.  Many  composi- 
tions by  young  pupils  trained  under  this  method  are  given. 


A  BRIEF  COURSE  IN  THE  HISTORY  OF 
EDUCATION 

By  PAUL  MONROE,  Ph.D.,  Professor  in  the  History  of  Education, 
Teachers  College,  Columbia  University.  8vo.  Cloth,  xviii  +  409 
pages.  $1.2$ 

This  is  practically  a  condensation  of  Professor  Monroe's  "  Text- 
book in  the  History  of  Education,"  issued  more  than  two  years  ago, 
and  still  the  most  extensive  work  on  the  subject  in  English.  The 
present  abbreviation  has  been  made  in  answer  to  the  demands  of 
normal  schools  and  teachers'  training  classes  which  have  not  the 
time  to  devote  to  the  study  of  the  larger  text.  Nevertheless  it  treats 
of  all  the  general  periods,  and  of  most  of  the  topics  discussed  in  th« 
larger  work. 


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UNIVERSITY  OF  CALIFORNIA  LIBRARY 

Los  Angeles 
This  book  is  DUE  on  the  last  date  stamped  below. 


OCT 


SUBJECT  TO  FINE  IF  NfcT 

ftPR    41943PUCATION 


Fft  2?  *83'8 
EDjPSYCH  I 


RETURNED  TO 

LIBRARY 


M 

a. 


Form  L9-40m-7,'56(C790s4)444 


of  child-development :  the  transitional,  the  formative,  the  adolescent. 
Part  V  considers  educational  values  and  the  necessity  of  ideals  in 
the  educative  process,  and  Part  VI  concludes  with  the  technique 
of  teaching. 

THE   MACMILLAN   COMPANY 

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Education 
.Library 

LB 
160? 
D36p 
v.2 


